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Compactness in locales and in formal topology.

Vickers, Steven (2005) Compactness in locales and in formal topology. Annals of Pure and Applied Logic, 137 (1-3). pp. 413-438. ISSN 0168-0072

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URL of Published Version: http://www.science-direct.com/science?_ob=ArticleURL&_udi=B6TYB-4GDBT1P-2&_user=122868&_coverDate=01%2F31%2F2006&_rdoc=20&_fmt=high&_orig=browse&_srch=doc-info(%23toc%235614%232006%23998629998%23609166%23FLP%23display%23Volume)&_cdi=5614&_sort=d&_docancho

Identification Number/DOI: doi:10.1016/j.apal.2005.05.028

If a locale is presented by a "flat site", it is shown how its frame can be presented by generators and relations as a dcpo. A necessary and suffcient condition is derived for compactness of the locale (and also forits openness). Although its derivation uses impredicative constructions, it is also shown predicatively using the inductive generation of formal topologies. A predicative proof of the binary Tychonoff theorem is given,including a characterization of the finite covers of the product by basic opens. The discussion is then related to the double powerlocale.

Type of Work:Article
Date:15 June 2005 (Publication)
School/Faculty:Schools (1998 to 2008) > School of Computer Science
Department:Computer Science
Subjects:Q Science (General)
QA Mathematics
Institution:University of Birmingham
Copyright Holders:Elsevier
ID Code:178
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