Factorization of mappings of topological spaces and homomorphisms of topological groups in accordance with weight and dimension \(\text{ind}\)
type: Item
instance of: scholarly article
title: Factorization of mappings of topological spaces and homomorphisms of topological groups in accordance with weight and dimension \(\text{ind}\)
zbMATH Open document ID: 0844.54023
DOI: 10.1007/BF02368674
author: Yanyan Li
published in: Journal of Mathematical Sciences (New York)
publication date: 1996-05-21T00:00:00Z
review text: Given a continuous mapping \(f : X \to Y\) of a compact space \(X\) to \(Y\), there exist a compact space \(Z\) and continuous mappings \(g : X \to Z\) and \(h : Z \to Y\) such that \(f = h \circ g\), \(Z = g(X)\), \(w(Z) \leq w (Y)\) and \(\dim Z \leq \dim Y\). This factorization theorem of Mardešić is also valid for the large inductive dimension Ind (B. A. Pasynkov) and for the small inductive dimension ind (I. M. Leibo). The author proves certain analogues of the Mardešić factorization theorem for the dimension ind. He shows in particular that all continuous mappings of hereditarily Lindelöf spaces can be factorized in accordance with the weight and the small inductive dimension. A similar assertion is valid for continuous homomorphisms of hereditarily Lindelöf topological groups (and of Lindelöf \(\Sigma\)-groups, too).
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54B35
zbMATH DE Number: 862254
zbMATH Keywords: factorization theorem
zbMATH Keywords: large inductive dimension
zbMATH Keywords: small inductive dimension
zbMATH Keywords: hereditarily Lindelöf spaces
zbMATH Keywords: weight
zbMATH Keywords: hereditarily Lindelöf topological groups
reviewed by: Mikhail Tkachenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 862254