On inductive dimensions
type: Item
instance of: scholarly article
title: On inductive dimensions
zbMATH Open document ID: 0559.54030
author: Vitalij A. Chatyrko
published in: Moscow University Mathematics Bulletin
publication date: 1983-01-01T00:00:00Z
review text: The author defines inductive dimension \(\sigma\) Ind as \(\sigma\) Ind X\(=- 1\) iff \(X=\emptyset\). Assume that the class of spaces X with \(\sigma\) Ind X\(<\alpha\) is already defined. Then \(\sigma Ind X\leq \alpha\) if X can be decomposed as countable sum of closed subsets \(F_ i\), \(i=1,2,..\). with the property: for each pair of disjoint closed subsets A and B of X there exist partitions \(C_ i\) in \(F_ i\) between \(A\cap F_ i\) and \(B\cap F_ i\) with \(\sigma Ind C_ i<\alpha\), \(i=1,2,... \). Analogously we get a definition of \(\sigma_ fInd\) if the word ''countable'' above is changed with the word ''finite''. If the set B changes with a point then we get the definitions of \(\sigma\) ind and \(\sigma_ find\) respectively. The author establishes some facts concerning the above mentioned notions. In particular some relations are obtained between the inductive dimensions and the classical ''dim'' and ''Ind'' and also some factorization theorems and assertions concerning some compact extensions and universal spaces. The author investigates the problem for the verification of the equality \(\sigma\) Ind X\(=\sigma Ind \beta X\) of any normal space X.
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 3892176
zbMATH Keywords: factorization theorems
zbMATH Keywords: compact extensions
zbMATH Keywords: universal spaces
MaRDI profile type: Publication
description: scientific article