Embeddings into pseudocompact spaces of countable tightness.
type: Item
instance of: scholarly article
title: Embeddings into pseudocompact spaces of countable tightness.
zbMATH Open document ID: 1041.54003
author: Angelo Bella
author: O. Pavlov
published in: Topology and its Applications
publication date: 2004-03-14T00:00:00Z
full work available at URL: https://polipapers.upv.es/index.php/AGT/article/view/1958
review text: Under the existence of scales of cardinality \(\omega_1\) which is implied by CH, the following important result is proved. Let \({\mathfrak F}\) be a free filter on \(\omega\). We assume that \({\mathfrak F}\) has a base which is well ordered by \(\subset^*\) of type \(\omega_1\). Then there exists a pseudocompact \(0\)-dimensional \(T_1\)-space of countable tightness which has a closed subspace homeomorphic to \(\omega\cup\{{\mathfrak F}\}\). The symbol \(\subset^*\) means \(B- A\) is finite. Moreover, two existence theorems are stated under CH that are concerned with pseudocompact Tikhonov spaces of countable tightness. If \(p\in \beta\omega- \omega\) is a P-point (i.e., if every \(G_\delta\) which contains a point \(a\) is a neighborhood of \(a\), then \(a\) is a P-point), then there exists a pseudocompact Tikhonov space of countable tightness which contains a closed copy of \(\omega\cup\{p\}\subset \beta\omega\). \(\beta\omega\) is the Čech compactification of \(\omega\). Another one is: there exists a pseudocompact Tikhonov space of countable tightness which contains a non-discrete extremally disconnected subspace.
reviewed by: Kiyoshi Iseki
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54G05
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 2056824
zbMATH Keywords: Countable tightness
zbMATH Keywords: Countable fan tightness
zbMATH Keywords: Sequential spaces
zbMATH Keywords: Pseudocompactness
zbMATH Keywords: P-points
zbMATH Keywords: Extremally disconnected spaces
MaRDI profile type: Publication
OpenAlex ID: W1989403000
cites work: Q4374681
cites work: Q4955943
cites work: \(F\)-points in countably compact spaces
cites work: Applications of maximal topologies
cites work: Q5186348
cites work: Q4150804
cites work: Countably Compact, Locally Countable T 2 -Spaces
DOI: 10.1016/J.TOPOL.2003.03.001
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description: scientific article; zbMATH DE number 2056824