Embedding compact spaces into compact spaces with few regular open Baire subsets
type: Item
instance of: scholarly article
title: Embedding compact spaces into compact spaces with few regular open Baire subsets
zbMATH Open document ID: 0913.54017
DOI: 10.1016/S0166-8641(97)00032-1
author: George Delistathis
published in: Topology and its Applications
publication date: 1999-06-01T00:00:00Z
review text: \textit{V. V. Fedorchuk} [Sov. Math., Dokl. 15(1974), 1272-1275 (1975); translation from Dokl. Akad. Nauk SSSR 218, 50-53 (1974; Zbl 0355.54013)] constructed a compact first countable space with only two regular open (regular closed) Baire subsets. In the paper under review, the author presents a general construction of spaces with these properties. He shows that, given a compact Hausdorff space \(X\), there exists a compact Hausdorff space \(Y\) such that \(X\) is a retract of \(Y\) and if \(F\) is a regular closed (or regular open) Baire subset of \(Y\), then \(F\) is open (closed). Moreover, if \(X\) is a continuum, \(Y\) is a continuum as well and \(Y\) has only two regular closed (or regular open) Baire subsets.
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54G15
Mathematics Subject Classification ID: 54C15
zbMATH DE Number: 1103053
zbMATH Keywords: embedding
zbMATH Keywords: retraction
zbMATH Keywords: compact space
zbMATH Keywords: continuum
zbMATH Keywords: Baire set
zbMATH Keywords: regular open set
zbMATH Keywords: regular closed set
zbMATH Keywords: zero set
reviewed by: Zbigniew Karno
MaRDI profile type: Publication
cites work: Q3713147
cites work: Q3994935
cites work: Q4127036
full work available at URL: s0166-8641(97)00032-1
OpenAlex ID: W2023024834
description: scientific article; zbMATH DE number 1103053