A note on the Prabir Roy space
type: Item
instance of: scholarly article
title: A note on the Prabir Roy space
zbMATH Open document ID: 0723.54033
DOI: 10.1016/0166-8641(90)90095-J
published in: Topology and its Applications
publication date: 1990-01-01T00:00:00Z
review text: Avoiding the continuum hypothesis, the author constructs a complete metric space with a basis of cardinality \(\aleph_ 1\), small inductive dimension \(ind(P)=0\) and large inductive dimension \(Ind(P)=1\). In so doing the author answers a question of \textit{Kunen} and \textit{van Douwen} and provides a slight generalization which includes a similar example due to \textit{J. Kulesza}. The first example of a metric space whose small and large inductive dimensions differ was announced in 1962 by \textit{P. Roy}, however such examples remain very scarce in the literature and are among the most complicated of all examples in topology in particular such examples must necessarily be nonseparable. The author's construction and proofs use the notions of fast sequences, large trees, and the Moore metrization theorem.
reviewed by: D.M.Rohm
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54G15
Mathematics Subject Classification ID: 03E65
Mathematics Subject Classification ID: 54F50
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 4192633
zbMATH Keywords: not strongly zero-dimensional spaces
zbMATH Keywords: complete metric spaces
zbMATH Keywords: gap metric spaces
zbMATH Keywords: inductive dimension
zbMATH Keywords: large trees
author: A. J. Ostaszewski
MaRDI profile type: Publication
cites work: Q4150804
cites work: Q4185470
cites work: Q3675176
cites work: An example in the dimension theory of metrizable spaces
cites work: Q3678306
cites work: Q4069959
cites work: Failure of equivalence of dimension concepts for metric spaces
cites work: Nonequality of Dimensions for Metric Spaces
cites work: Combinatorial problems on trees: partitions, \(\Delta\)-systems and large free subtrees
full work available at URL: 0166-8641(90)90095-j
OpenAlex ID: W2082667495
description: scientific article; zbMATH DE number 4192633