Dimension theory
type: Item
instance of: scholarly article
title: Dimension theory
zbMATH Open document ID: 0481.54020
DOI: 10.1007/BF01091964
author: V. V. Filippov
author: B. A. Pasynkov
author: V. V. Fedorchuk
published in: Journal of Soviet Mathematics
publication date: 1982-01-01T00:00:00Z
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54-02
zbMATH DE Number: 3755470
zbMATH Keywords: Bibliography
zbMATH Keywords: dimensional invariant
zbMATH Keywords: monotonicity
zbMATH Keywords: sum theorems
zbMATH Keywords: mappings
zbMATH Keywords: products
zbMATH Keywords: factorization theorems
zbMATH Keywords: universal spaces
zbMATH Keywords: compactification
zbMATH Keywords: inverse spectra
zbMATH Keywords: Cantor manifolds
zbMATH Keywords: axiomatic
zbMATH Keywords: metric dimensions
zbMATH Keywords: uniform and proximity spaces
zbMATH Keywords: dimensional-like functions
zbMATH Keywords: infinite-dimensional spaces
MaRDI profile type: Publication
cites work: Q5678165
cites work: Properties of the topological and uniform dimension in terms of rings of continuous functions
cites work: ON THE DIMENSION THEORY OF METRIZABLE SPACES WITH PERIODIC HOMEOMORPHISMS
cites work: Q5678188
cites work: Q4043773
cites work: Q4085717
cites work: Q5557731
cites work: Remark on the dimension of metric spaces
cites work: Q3858921
cites work: Q3253033
cites work: Q4197733
cites work: Q4179535
cites work: Q4110320
cites work: On a theorem of Hurewicz
cites work: Q4043778
cites work: Q5338737
cites work: Q5621779
cites work: Q4772403
cites work: ON THE EMBEDDING OF COUNTABLE PRODUCTS OF SEPARABLE METRIC SPACES IN WEAKLY INFINITE-DIMENSIONAL COMPACTA
cites work: Q3292113
cites work: Q3244828
cites work: Q3213863
cites work: Q4776579
cites work: Q3850442
cites work: Q5518105
cites work: Spaces of transfinite dimensionality
cites work: Размерность метрических пространств и ретракция
cites work: Q4052855
cites work: Q4095558
cites work: Q5344739
cites work: Q5537079
cites work: Extension of continuous maps and the factorization theorem
cites work: Q5586019
cites work: Q4772404
cites work: Q5607709
cites work: Q5618760
cites work: Q5593777
cites work: Q4048235
cites work: Q3879935
cites work: Q4197734
cites work: Q4056707
cites work: Q4076498
cites work: Equality of dimensions of completely normal compact spaces
cites work: Q5341862
cites work: Q5327714
cites work: Q5726246
cites work: Q5560894
cites work: Q5537072
cites work: Q5577656
cites work: Q5605712

Dimension theory (cites work)
cites work: Q5612307

Dimension theory (cites work)
cites work: Q5649106

Dimension theory (cites work)
cites work: Q4775155

Dimension theory (cites work)
cites work: Q4101156

Dimension theory (cites work)
cites work: Q4122498

Dimension theory (cites work)
cites work: Q5604373

Dimension theory (cites work)
cites work: Q5561734

Dimension theory (cites work)
cites work: On completely closed mappings

Dimension theory (cites work)
cites work: An example of a perfectly normal bicompactum with no intermediate dimensions

Dimension theory (cites work)
cites work: Q4150336

Dimension theory (cites work)
cites work: Q3254873

Dimension theory (cites work)
cites work: Q3264658

Dimension theory (cites work)
cites work: Q3281618

Dimension theory (cites work)
cites work: Q5510540

Dimension theory (cites work)
cites work: Q3254872

Dimension theory (cites work)
cites work: Q5518106

Dimension theory (cites work)
cites work: Q5585148

Dimension theory (cites work)
cites work: Q3260165

Dimension theory (cites work)
cites work: Q5580156

Dimension theory (cites work)
cites work: Q5583680

Dimension theory (cites work)
cites work: Q4776606

Dimension theory (cites work)
cites work: Q4097895

Dimension theory (cites work)
cites work: Q4097900

Dimension theory (cites work)
cites work: Q4155474

Dimension theory (cites work)
cites work: Q5614449

Dimension theory (cites work)
cites work: Q5604374

Dimension theory (cites work)
cites work: Q5180569

Dimension theory (cites work)
cites work: Q4043777

Dimension theory (cites work)
cites work: Q5616666

Dimension theory (cites work)
cites work: Q3847398

Dimension theory (cites work)
cites work: Q5612308

Dimension theory (cites work)
cites work: Q5681284

Dimension theory (cites work)
cites work: AXIOMATICS OF THE DIMENSION OF METRIC SPACES

Dimension theory (cites work)
cites work: Q4150334

Dimension theory (cites work)
cites work: Covering dimension modulo a class of spaces

Dimension theory (cites work)
cites work: Kernels in Dimension Theory

Dimension theory (cites work)
cites work: An Example in Dimension Theory

Dimension theory (cites work)
cites work: On closed mappings, bicompact spaces and a problem of P. Aleksandrov

Dimension theory (cites work)
cites work: Spaces Of Dimension Zero

Dimension theory (cites work)
cites work: Zur Dimensionstheorie der Kompakten im \(R^n\)

Dimension theory (cites work)
cites work: Q5658821

Dimension theory (cites work)
cites work: Q3246717

Dimension theory (cites work)
cites work: Q3844870

Dimension theory (cites work)
cites work: Q4070025

Dimension theory (cites work)
cites work: Ein eindimensionales Kompaktum in $E^3$, das sich nicht lagetreu in die Mengersche Universalkurve einbetten läβt

Dimension theory (cites work)
cites work: Zur Lage null- und eindimensionaler Punktmengen im $E^3$

Dimension theory (cites work)
cites work: On the non-monotony of dimension

Dimension theory (cites work)
cites work: Uniformization of topological spaces with small inductive dimension zero

Dimension theory (cites work)
cites work: A Metric Characterizing Cech Dimension Zero

Dimension theory (cites work)
cites work: Metrization of spaces having Čech dimension zero

Dimension theory (cites work)
cites work: Four Metric Conditions Characterizing Cech Dimension Zero

Dimension theory (cites work)
cites work: Dimension theory in zero-set spaces

Dimension theory (cites work)
cites work: A New Covering Dimension Function for Uniform Spaces

Dimension theory (cites work)
cites work: Axiomatic characterisations of dimension

Dimension theory (cites work)
cites work: The Dimension of Inverse Limits

Dimension theory (cites work)
cites work: Q4150833

Dimension theory (cites work)
cites work: Q4061671

Dimension theory (cites work)
cites work: Q5333708

Dimension theory (cites work)
cites work: Q5532992

Dimension theory (cites work)
cites work: Einige Beziehungen der Richtungsdimension zu den klassischen Dimensionsbegriffen der allgemeinen Topologie

Dimension theory (cites work)
cites work: Q3213866

Dimension theory (cites work)
cites work: Q5644774

Dimension theory (cites work)
cites work: Q4113117

Dimension theory (cites work)
cites work: Regular mappings and dimension

Dimension theory (cites work)
cites work: Certain transformations which lower dimension

Dimension theory (cites work)
cites work: On the dimension of products

Dimension theory (cites work)
cites work: Sur la compactification des espaces métriques

Dimension theory (cites work)
cites work: Q3281611

Dimension theory (cites work)
cites work: Dimension of the square of a space

Dimension theory (cites work)
cites work: Q4072510

Dimension theory (cites work)
cites work: On the Dimension of Hereditarily Normal Spaces

Dimension theory (cites work)
cites work: Dimension preserving compactifications allowing extensions of continuous functions

Dimension theory (cites work)
cites work: Extensions of Mappings into n-Cubes

Dimension theory (cites work)
cites work: A \(\sigma\)-initially locally finite characterization of large inductive dimension for metric spaces

Dimension theory (cites work)
cites work: A Characterization of Covering Dimension for Collectionwise Normal Spaces

Dimension theory (cites work)
cites work: Q4776603

Dimension theory (cites work)
cites work: Q4082015

Dimension theory (cites work)
cites work: Concerning the Shapes of Finite-Dimensional Compacta

Dimension theory (cites work)
cites work: Q4056733

Dimension theory (cites work)
cites work: SOME RESULTS CONCERNING THE DIMENSION OF THE SPACE OF COMPACT SUBSETS OF THE UNIT INTERVAL

Dimension theory (cites work)
cites work: Non-Archimedean Metrics in Topology

Dimension theory (cites work)
cites work: On a Metric that Characterizes Dimension

Dimension theory (cites work)
cites work: Extension of mappings on metric spaces

Dimension theory (cites work)
cites work: Dimension der Bahnen lokal kompakter Gruppen

Dimension theory (cites work)
cites work: On the characterization of the dimension of a compact metric space K by the representing matrices of C(K)

Dimension theory (cites work)
cites work: Q3228116

Dimension theory (cites work)
cites work: Q5831050

Dimension theory (cites work)
cites work: Q3279816

Dimension theory (cites work)
cites work: Compactifications of Dimension Zero

Dimension theory (cites work)
cites work: Q5526603

Dimension theory (cites work)
cites work: An Infinite-Dimensional Compactum with no Positive-Dimensional Compact Subsets-A Simpler Construction

Dimension theory (cites work)
cites work: Each Strongly Infinite-Dimensional Compactum Contains a Hereditarily Infinite-Dimensional Compact Subset

Dimension theory (cites work)
cites work: D-dimension. I: A new transfinite dimension

Dimension theory (cites work)
cites work: D-dimension. II: Separable spaces and compactifications

Dimension theory (cites work)
cites work: A lower bound for transfinite dimension

Dimension theory (cites work)
cites work: Irreducible continua of higher dimension

Dimension theory (cites work)
cites work: Concerning irreducible continua of higher dimension

Dimension theory (cites work)
cites work: Dimension raising maps in topological algebra

Dimension theory (cites work)
cites work: One dimensional coset spaces

Dimension theory (cites work)
cites work: On finite-dimensional uniform spaces

Dimension theory (cites work)
cites work: Embeddings of inverse limits

Dimension theory (cites work)
cites work: Q3289533

Dimension theory (cites work)
cites work: On finite-dimensional uniform spaces. II

Dimension theory (cites work)
cites work: A Metric Characterization of Zero-Dimensional Spaces

Dimension theory (cites work)
cites work: On the extensibility of mappings, their local properties and some of their connections with the dimension theory

Dimension theory (cites work)
cites work: Dendrites, dimension, and the inverse arc function

Dimension theory (cites work)
cites work: A note on the inductive dimension of product spaces

Dimension theory (cites work)
cites work: Open and closed mappings and compactification

Dimension theory (cites work)
cites work: Proper Mappings and Dimension

Dimension theory (cites work)
cites work: Mappings and dimension in metric spaces

Dimension theory (cites work)
cites work: Proper Mappings and the Minimum Dimension of a Compactification of a Space

Dimension theory (cites work)
cites work: On the inductive dimension of product spaces

Dimension theory (cites work)
cites work: On the covering dimension of product spaces

Dimension theory (cites work)
cites work: On the covering dimension of certain product spaces

Dimension theory (cites work)
cites work: On a sum theorem in dimension theory

Dimension theory (cites work)
cites work: On homotopically stable points and product spaces

Dimension theory (cites work)
cites work: On $LC^n$ metric spaces

Dimension theory (cites work)
cites work: On a problem of Alexandroff concerning the dimension of product spaces. I, II

Dimension theory (cites work)
cites work: Homological dimension and product spaces

Dimension theory (cites work)
cites work: A necessary and sufficient condition under which $\mathrm{dim} \left( {X \times Y} \right) = \mathrm{dim} X + \mathrm{dim} Y$

Dimension theory (cites work)
cites work: On Subset Theorems and the Dimension of Products

Dimension theory (cites work)
cites work: Q5639000

Dimension theory (cites work)
cites work: Q5681259

Dimension theory (cites work)
cites work: On the hyperspaces of hereditarily indecomposable continua

Dimension theory (cites work)
cites work: Remark on mappings not raising dimension of curves

Dimension theory (cites work)
cites work: Q4069968

Dimension theory (cites work)
cites work: A note on the dimension Dind

Dimension theory (cites work)
cites work: Imbedding of compact metric spaces into cubes

Dimension theory (cites work)
cites work: О независимости точек метрического пространства

Dimension theory (cites work)
cites work: Sur deux genres d'espaces complets

Dimension theory (cites work)
cites work: On compactifications of some subsets of Euclidean spaces

Dimension theory (cites work)
cites work: Fixations of sets in Euclidean spaces

Dimension theory (cites work)
cites work: Dimension and mappings of spaces with finite deficiency

Dimension theory (cites work)
cites work: Dimension inequalities for unions and mappings of separable metric spaces

Dimension theory (cites work)
cites work: Dimensions of irreducible continua and fixations of components in compact spaces

Dimension theory (cites work)
cites work: Q4776600

Dimension theory (cites work)
cites work: On Imbedding Finite-Dimensional Metric Spaces

Dimension theory (cites work)
cites work: An Imbedding Theorem for Metric Spaces

Dimension theory (cites work)
cites work: Q4097894

Dimension theory (cites work)
cites work: Q4112611

Dimension theory (cites work)
cites work: Compact Subsets of R n and Dimension of Their Projections

Dimension theory (cites work)
cites work: Q5510553

Dimension theory (cites work)
cites work: Test Spaces for Metric Spaces

Dimension theory (cites work)
cites work: Test Spaces for Normal Spaces

Dimension theory (cites work)
cites work: A note on covering dimension of paracompact spaces

Dimension theory (cites work)
cites work: Q5850148

Dimension theory (cites work)
cites work: On the product of paracompact spaces

Dimension theory (cites work)
cites work: On the dimension of the product of Tychonoff spaces

Dimension theory (cites work)
cites work: On the dimension of the product of topological spaces

Dimension theory (cites work)
cites work: On some types of polyhedra

Dimension theory (cites work)
cites work: Some theorems in dimension theory for non-separable spaces

Dimension theory (cites work)
cites work: Finite-to-one closed mappings and dimension, I

Dimension theory (cites work)
cites work: Finite-to-one closed mappings and dimension, II

Dimension theory (cites work)
cites work: On the dimension of product spaces

Dimension theory (cites work)
cites work: Note on metrizability and $n$-dimensionality

Dimension theory (cites work)
cites work: Remarks on Katětov's uniformly $O$-dimensional mappings

Dimension theory (cites work)
cites work: Finite-to-one closed mappings and dimension, III

Dimension theory (cites work)
cites work: Finite-to-one closed mappings and dimension, IV

Dimension theory (cites work)
cites work: Mappings defined on 0-dimensional spaces and dimension theory

Dimension theory (cites work)
cites work: Dimension-theoretical structure of locally compact groups

Dimension theory (cites work)
cites work: A Nagata's metric which characterizes dimension and enlarges distance

Dimension theory (cites work)
cites work: Monotone sequence of $O$-dimensional subsets of metric spaces

Dimension theory (cites work)
cites work: Q5630369

Dimension theory (cites work)
cites work: Perfect class of spaces

Dimension theory (cites work)
cites work: A Study of Metric-Dependent Dimension Functions

Dimension theory (cites work)
cites work: On a relation between dimension and metrization

Dimension theory (cites work)
cites work: Note on dimension theory

Dimension theory (cites work)
cites work: On imbedding a metric space in a product of one-dimensional spaces

Dimension theory (cites work)
cites work: On countable-dimensional spaces

Dimension theory (cites work)
cites work: Q3258685

Dimension theory (cites work)
cites work: Note on dimension theory for metric spaces

Dimension theory (cites work)
cites work: A theorem of dimension theory

Dimension theory (cites work)
cites work: On a universal n-dimensional set for metric spaces.

Dimension theory (cites work)
cites work: Two remarks on dimension theory for metric spaces

Dimension theory (cites work)
cites work: On a metric characterizing dimension

Dimension theory (cites work)
cites work: On rings of continuous functions and the dimension of metric spaces

Dimension theory (cites work)
cites work: A remark on general imbedding theorems in dimension theory

Dimension theory (cites work)
cites work: Q5548810

Dimension theory (cites work)
cites work: Examples concerning sum properties for metric-dependent dimension functions

Dimension theory (cites work)
cites work: Semi-Compact Spaces and Dimension

Dimension theory (cites work)
cites work: On the dimension of semi-compact spaces and their quasi-components

Dimension theory (cites work)
cites work: Inductive invariants of closed extensions of mappings

Dimension theory (cites work)
cites work: A subset theorem in dimension theory

Dimension theory (cites work)
cites work: Some properties of fundamental dimension

Dimension theory (cites work)
cites work: The Sorgenfrey plane in dimension theory

Dimension theory (cites work)
cites work: Q4127051

Dimension theory (cites work)
cites work: Uniforme Räume mit einer linear geordneten Basis

Dimension theory (cites work)
cites work: A note on the covering dimension of Lasnev spaces

Dimension theory (cites work)
cites work: On cohomological dimension for paracompact spaces, I

Dimension theory (cites work)
cites work: A Perfectly Normal Countably Compact Scattered Space which is not Strongly Zero-Dimensional

Dimension theory (cites work)
cites work: Dimension of metric spaces and Hilbert’s problem 13

Dimension theory (cites work)
cites work: A conjecture of J. Nagata on dimension and metrization

Dimension theory (cites work)
cites work: Covering dimension in general spaces

Dimension theory (cites work)
cites work: Q5683915

Dimension theory (cites work)
cites work: Some order properties of coverings of finite-dimensional spaces

Dimension theory (cites work)
cites work: A Sum Theorem for Local Inductive Dimension

Dimension theory (cites work)
cites work: Dimension Theory of M -Spaces

Dimension theory (cites work)
cites work: Closed Covers, Dimension, and Quasi-Order Spaces

Dimension theory (cites work)
cites work: Q4107629

Dimension theory (cites work)
cites work: Addition and correction to the paper "On stability and products", Fund. Math. 93 (1976), pp. 81-95

Dimension theory (cites work)
cites work: Q4150335

Dimension theory (cites work)
cites work: On a weak sum theorem in dimension theory

Dimension theory (cites work)
cites work: On a theorem of W. Hurewicz on mappings which lower dimension

Dimension theory (cites work)
cites work: Q5586022

Dimension theory (cites work)
cites work: Q4766224

Dimension theory (cites work)
cites work: Q4159938

Dimension theory (cites work)
cites work: Q4104999

Dimension theory (cites work)
cites work: Metric dimension and equivalent metrics

Dimension theory (cites work)
cites work: Characterization of dimension in terms of the existence of a continuum

Dimension theory (cites work)
cites work: Realizability of Metric-Dependent Dimensions

Dimension theory (cites work)
cites work: Dimension and the Whitney subcontinua of C(X)

Dimension theory (cites work)
cites work: An axiomatic characterization of the large inductive dimension for metric spaces

Dimension theory (cites work)
cites work: On extensions of mappings into $n$-cubes

Dimension theory (cites work)
cites work: Q3229077

Dimension theory (cites work)
cites work: Hyperspaces of the Inverse Limit Space

Dimension theory (cites work)
cites work: Q4076497

Dimension theory (cites work)
cites work: Some embeddings of infinite-dimensional spaces

Dimension theory (cites work)
cites work: Lebesgue Characterizations of Uniformity Dimension Functions

Dimension theory (cites work)
cites work: Other characterizations and weak sum theorems for metric-dependent dimension functions

Dimension theory (cites work)
cites work: A Scattered Space that is not Zero-Dimensional

Dimension theory (cites work)
cites work: Characterizations of uniformity-dependent dimension functions

Dimension theory (cites work)
cites work: The Dimension of the Convex Kernel and Points of Local Nonconvexity

Dimension theory (cites work)
cites work: Uniformly separating families of functions

Dimension theory (cites work)
cites work: General position for closed subsets of euclidean space

Dimension theory (cites work)
cites work: Note on a theorem for dimension

Dimension theory (cites work)
cites work: Q5180567

Dimension theory (cites work)
cites work: Q4062355

Dimension theory (cites work)
cites work: Q5667244

Dimension theory (cites work)
cites work: Q4123994

Dimension theory (cites work)
cites work: Q3293857

Dimension theory (cites work)
cites work: A modification of Morita's characterization of dimension

Dimension theory (cites work)
cites work: The Intersection Multiplicity of n-Dimensional Paracompact Spaces

Dimension theory (cites work)
cites work: Sums of finite-dimensional spaces

Dimension theory (cites work)
cites work: Dimension-Theoretic Properties of Completions

Dimension theory (cites work)
cites work: Finite-dimensional properties of infinite-dimensional spaces

Dimension theory (cites work)
cites work: A universal separable metric locally finite-dimensional space

Dimension theory (cites work)
cites work: Dimension and non-density preservation of mappings

Dimension theory (cites work)
cites work: A Lower Bound for the Dimension of Certain G δ Sets in Completely Normal Spaces

Dimension theory (cites work)
cites work: Q5676821

Dimension theory (cites work)
cites work: Monotone Mapping Properties of Hereditarily Infinite Dimensional Spaces

Dimension theory (cites work)
cites work: Sur l'enfilage et la fixation des ensembles compacts

Dimension theory (cites work)
cites work: P.R.-Regulated Systems of Notation and the Subrecursive Hierarchy Equivalence Property

Dimension theory (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf01091964

Dimension theory (OpenAlex ID)
OpenAlex ID: W4211155929