A homogeneous extremally disconnected countably compact space
type: Item
instance of: scholarly article
title: A homogeneous extremally disconnected countably compact space
zbMATH Open document ID: 0613.54027
DOI: 10.1016/0166-8641(87)90075-7
author: Jan van Mill
author: W. W. Comfort
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The authors prove (in ZFC) that there exist infinite homogeneous countably compact extremally disconnected spaces. (This contrasts to the previously known result that infinite homogeneous compact extremally disconnected spaces do not exist). They also produce, using Martin's axiom, two countably compact homogeneous extremally disconnected spaces whose product is not countably compact. Some related open questions are posed.
Mathematics Subject Classification ID: 54G05
Mathematics Subject Classification ID: 54G20
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 3992420
zbMATH Keywords: countable compactness
zbMATH Keywords: ZFC
zbMATH Keywords: infinite homogeneous countably compact extremally disconnected spaces
zbMATH Keywords: Martin's axiom
reviewed by: R. G. Woods
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90075-7
OpenAlex ID: W2041221831
cites work: Q5532970
cites work: Ultrafilters on a countable set
cites work: Q5544881
cites work: Ultrafilters: Some old and some new results
cites work: Q3741814
cites work: On the product of homogeneous spaces
cites work: Q4052073
cites work: Pseudocompactness and uniform continuity in topological groups
cites work: Homogeneity of βG if G is a topological group
cites work: Q3793341
cites work: Q4074056
cites work: Q5548170
cites work: Q5660881
cites work: Q3270120
cites work: Ultrafilters and Independent Sets
cites work: Q5636038
cites work: Q4083631
cites work: THE PRODUCT OF TOPOLOGICAL GROUPS AND EXTREMAL DISCONNECTEDNESS
cites work: Q4049278
description: scientific article; zbMATH DE number 3992420