Components of first-countability and various kinds of pseudoopen mappings
type: Item
instance of: scholarly article
title: Components of first-countability and various kinds of pseudoopen mappings
zbMATH Open document ID: 1209.54004
published in: Topology and its Applications
publication date: 2011-01-13T00:00:00Z
review text: Three subclasses of the well-known class of pseudoopen mappings are introduced (\(\omega\)-pseudoopen, strictly \(\omega\)-pseudoopen, almost \(\omega\)-pseudo\-open mappings). First countability of images of \(T_1\) spaces under these mappings is investigated. Let \(f:X\to Y\) be a continuous mapping from a \(T_1\) space \(X\) onto a regular pseudocompact space \(Y\). Then \(Y\) is first countable in each of the following cases: (1) \(f\) is \(\omega\)-pseudoopen, (2) \(f\) is almost \(\omega\)-pseudoopen, (3) \(X\) is metric and \(f\) is a pseudopen almost \(S\)-mapping (for any non-isolated point \(y\in Y\), \(f^{-1}(y)\) is separable). If \(f\) is strictly \(\omega\)-pseudopen, then \(f\) is biquotient. A Hausdorff topological group which is the image of a \(T_1\)-space under an \(\omega\)-pseudoopen mapping is metrizable.
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54D70
zbMATH DE Number: 5835748
zbMATH Keywords: pseudoopen mapping
zbMATH Keywords: biquotient mapping
zbMATH Keywords: almost \(S\)-mapping
zbMATH Keywords: first countability
zbMATH Keywords: metrizability
author: A. V. Arhangel'skii
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: j.topol.2010.10.013
OpenAlex ID: W1966892365
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DOI: 10.1016/J.TOPOL.2010.10.013
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description: scientific article; zbMATH DE number 5835748