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

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

Volume

160

Issue

12

Volume

160

Issue

12

Peer Reviewed

yes

Link to published version

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