Document Type
Article
Publication Date
8-2013
Publication Source
Topology and its Applications
Abstract
We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every Čech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense Gδ-subsets of Cantor cubes are subcompact.
Inclusive pages
1305–1312
ISBN/ISSN
0166-8641
Document Version
Preprint
Copyright
Copyright © 2013, Elsevier
Publisher
Elsevier
Volume
160
Issue
12
Peer Reviewed
yes
eCommons Citation
Fleissner, William; Tkachuk, Vladimir; and Yengulalp, Lynne, "Every Scattered Space is Subcompact" (2013). Mathematics Faculty Publications. 39.
https://ecommons.udayton.edu/mth_fac_pub/39
Comments
The document available for download is the authors' submitted manuscript, provided in compliance with the publisher's policy on self-archiving. Differences may exist between this document and the published version, which is available using the link provided. Permission documentation is on file.