On cardinal invariants of continuous images of topological groups
type: Item
instance of: scholarly article
title: On cardinal invariants of continuous images of topological groups
zbMATH Open document ID: 0791.22001
DOI: 10.1007/BF01874230
published in: Acta Mathematica Hungarica
publication date: 1994-01-13T00:00:00Z
review text: Sufficient conditions on a topological space \(X\) are indicated in order that the character \(\chi(p,X)\) and the tightness \(t(p,X)\) coincide at every point \(p\in X\). We state the main result: Theorem 1. If a compact space \(X\) is a continuous image of a dense subset in a product of \(\sigma\)-compact topological groups, then \(\chi(p,X)=t(p,X)\) for every point \(p\in X\). The paper contains also some more general assertions than theorem 1. At the end the author poses three open problems. We mention here Question 3: Suppose there exists a continuous mapping of a dense subspace of a \(\sigma\)-compact topological group \(H\) onto a Tychonoff cube \(I^ \tau\), \(\tau>\aleph_ 0\). Is there a continuous mapping of \(H\) onto \(I^ \tau\)?
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 480510
zbMATH Keywords: character
zbMATH Keywords: tightness
zbMATH Keywords: compact spaces
zbMATH Keywords: dense subsets
zbMATH Keywords: \(\sigma\)-compact topological groups
zbMATH Keywords: Tychonoff cube
author: Mikhail Tkachenko
reviewed by: Mihail I. Ursul
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01874230
OpenAlex ID: W2058570960
description: scientific article; zbMATH DE number 480510