Article
A Note on Irreducibility and Weak Covering Properties
Topology Proceedings
Document Type
Article
Publication Date
1-1-1984
Abstract
A space X is irreducible if every open cover of X has a minimal open refinement. Interest in irreducibility began when Arens and Dugendji used this property to show that metacompact countably compact spaces are compact. It was natural, then, to find out what other types of spaces would be irreducible and therefore compact in the presence of countable compactness or Lindelof in the presence of N1-compactness. …
It is shown in this paper that T1 δθ -refinable spaces and T1 weakly δθ-refinable spaces are irreducible. Since examples of Lindelof spaces that are neither T1 nor irreducible can be easily constructed, it is clear that the spaces must be T1 .
ISBN/ISSN
0146-4124
Document Version
Postprint
Copyright
Copyright © 1984, Topology Proceedings.
Publisher
Auburn University
Peer Reviewed
Yes
Disciplines
Citation Information
Joe Mashburn. "A Note on Irreducibility and Weak Covering Properties" Topology Proceedings Vol. 9 (1984) Available at: http://works.bepress.com/joe_mashburn/14/
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