Title

A Note on Irreducibility and Weak Covering Properties

Author(s)

Joe Mashburn, University of DaytonFollow

Document Type

Article

Publication Date

1984

Publication Source

Topology Proceedings

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

Comments

The document available for download is the accepted manuscript of the paper that appeared in Vol. 9 of Topology Proceedings. It is included in the repository with the permission of the publisher. Some differences may exist between this version and the published version; as such, researchers wishing to quote directly from this source are advised to consult the version of record, available online from the publisher.

Permission documentation is on file.

Copyright

Copyright © 1984, Topology Proceedings.

Publisher

Auburn University

Volume

9

Peer Reviewed

yes

eCommons Citation

Mashburn, Joe, "A Note on Irreducibility and Weak Covering Properties" (1984). Mathematics Faculty Publications. 27.
https://ecommons.udayton.edu/mth_fac_pub/27