Set-theoretic constructions of nonshrinking open covers
type: Item
instance of: scholarly article
title: Set-theoretic constructions of nonshrinking open covers
zbMATH Open document ID: 0574.54020
DOI: 10.1016/0166-8641(85)90077-X
author: Amer Bešlagić
author: Mary Ellen Rudin
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: The authors give two interesting examples of topological spaces. (1) Let \(\kappa\) be an infinite regular cardinal. Then \(\diamond^{++}\) implies the existence of a Hausdorff, strongly zero-dimensional, collectionwise normal, \(\kappa\)-ultraparacompact, P-space with the following property: Every increasing open cover has a clopen shrinking, but there is an open cover which has no closed shrinking. (2) Let \(\kappa\) be an uncountable regular cardinal. Then \(\Delta\) implies the existence of a Hausdorff, collectionwise normal, countably ultraparacompact P-space, which has a strictly increasing open cover having no shrinking, each member of which is the union of at most \(\kappa\) closed sets.
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 03E45
Mathematics Subject Classification ID: 54G10
zbMATH DE Number: 3917220
zbMATH Keywords: shrinkable normal P-space
zbMATH Keywords: \(V=L\)
zbMATH Keywords: Hausdorff, strongly zero-dimensional, collectionwise normal, \(\kappa \) -ultraparacompact, P-space
zbMATH Keywords: clopen shrinking
zbMATH Keywords: Hausdorff, collectionwise normal, countably ultraparacompact P-space
zbMATH Keywords: strictly increasing open cover
reviewed by: Rudolf Z. Domiaty
MaRDI profile type: Publication
cites work: Q4150804
cites work: Applications of Shrinkable Covers
cites work: Q3673651
cites work: The Shrinking Property
cites work: Q3036256
cites work: A Class of Countably Paracompact Spaces
cites work: On Countably Paracompact Spaces
cites work: A normal space X for which X×I is not normal
cites work: $\aleph $-Dowker spaces
cites work: Q3681543
cites work: Products of normal spaces with metric spaces
cites work: Q3894629
cites work: Q4069465
cites work: Q4180937
cites work: An Extremally Disconnected Dowker Space
cites work: Two More Hereditarily Separable Non-Lindelöf Spaces
cites work: Countable Paracompactness and Souslin's Problem
cites work: A Construction of a Dowker Space
cites work: Small Dowker spaces
cites work: On Countably Compact, Perfectly Normal Spaces
cites work: The combinatorial principle ⋄#
cites work: Son of George and V = L
cites work: A normal screenable non-paracompact space
cites work: Set theory. An introduction to independence proofs
description: scientific article; zbMATH DE number 3917220