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Article
Every Scattered Space is Subcompact
Topology and its Applications
  • William Fleissner, University of Kansas
  • Vladimir Tkachuk, Universidad Autónoma Metropolitana
  • Lynne Yengulalp, University of Dayton
Document Type
Article
Publication Date
8-1-2013
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
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.

Publisher
Elsevier
Peer Reviewed
Yes
Citation Information
William Fleissner, Vladimir Tkachuk and Lynne Yengulalp. "Every Scattered Space is Subcompact" Topology and its Applications Vol. 160 Iss. 12 (2013)
Available at: http://works.bepress.com/lynne_yengulalp/8/