A construction involving inverse limits
type: Item
instance of: scholarly article
title: A construction involving inverse limits
zbMATH Open document ID: 1479.54048
published in: Topology and its Applications
publication date: 2021-09-27T00:00:00Z
review text: Recall that a topological space is called an \(F\)-space if any two disjoint open \(F_\sigma\) subsets have disjoint closures; and that a continuous mapping \(f:X\to Y\) is called irreducible if \(f[X] = Y\) and \(f[F] = Y\) implies \(F = X\) for every closed set \(F\subset X\). The main result (Theorem 4.3) states that for any compact space \(X\) there exists a compact \(F\)-space \(FX\) and an irreducible mapping \(f:FX\to X\) such that the weight of \(FX\) is minimal possible, that is, \(w(FX) = w(X)^\omega\). The space \(FX\) above is constructed using inverse limits. The result is very clearly motivated and put into the right context of related results.
reviewed by: Marek Cúth
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54G05
Mathematics Subject Classification ID: 06E05
Mathematics Subject Classification ID: 54B10
zbMATH DE Number: 7401480
zbMATH Keywords: inverse limits
zbMATH Keywords: \(F\)-spaces
zbMATH Keywords: extremally disconnected
zbMATH Keywords: irreducible maps
zbMATH Keywords: zero-dimensional
zbMATH Keywords: compact
author: Aleksander Błaszczyk
MaRDI profile type: Publication
full work available at URL: j.topol.2020.107494
OpenAlex ID: W3111191415
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DOI: 10.1016/J.TOPOL.2020.107494
description: scientific article; zbMATH DE number 7401480