Admissibility, homeomorphism extension and the AR-property in topological linear spaces
type: Item
instance of: scholarly article
title: Admissibility, homeomorphism extension and the AR-property in topological linear spaces
zbMATH Open document ID: 0774.55002
DOI: 10.1016/0166-8641(92)90121-F
author: Jos Van der Bijl
author: Tadeusz Dobrowolski
author: Jan van Mill
author: K. P. Hart
published in: Topology and its Applications
publication date: 1993-04-01T00:00:00Z
review text: One of the main problems of the topology of vector spaces is to prove that every linear space has the absolute extension property (AE- property). Some relative properties are considered in the paper. One of them is the so-called homeomorphism extension property (HEP). It is proved that HEP for finite-dimensional compacta holds in every infinite- dimensional complete linear space and, even more, in every non-\(\sigma\)- compact linear space. Also it is proved that if there is a counterexample to the AE-conjecture for linear spaces then there is a counterexample to HEP. The other is so-called an admissibility which is very closely to the extension property for compact spaces. It is proved that HEP implies admissibility. The question ``Is every linear space admissible?'' is discussed.
Mathematics Subject Classification ID: 55M15
Mathematics Subject Classification ID: 57N17
Mathematics Subject Classification ID: 54H13
Mathematics Subject Classification ID: 54C55
zbMATH DE Number: 149087
zbMATH Keywords: absolute retract
zbMATH Keywords: topological linear space
zbMATH Keywords: homeomorphism extension
reviewed by: Alexander Dranishnikov
MaRDI profile type: Publication
cites work: A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandrof's problem
cites work: The Role of Countable Dimensionality in the Theory of Cell-Like Relations
cites work: On spaces of measurable functions
cites work: Q4060144
cites work: Some Applications of The Topological Characterizations of the Sigma-Compact Spaces l 2 f and &#8721
cites work: On Extending Mappings into Nonlocally Convex Linear Metric Spaces
cites work: Extending Homeomorphisms and Applications to Metric Linear Spaces Without Completeness
cites work: Q3903491
cites work: An extension of Tietze's theorem
cites work: Eine Bemerkung über die Räume vom Typus (F)
cites work: Q4775149
cites work: Q5522732
cites work: Some Topological Properties of Convex Sets
cites work: Leray-Schauder theory without local convexity
cites work: Characterizing the Topology of Infinite-Dimensional σ-Compact Manifolds
cites work: Q5516366
cites work: Linear Spaces, Absolute Retracts, and the Compact Extension Property
cites work: Another Counterexample in ANR Theory
cites work: Q3812929
description: scientific article; zbMATH DE number 149087