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Constructive Notions of Compactness in Apartness Spaces

We present three criteria for compactness in the context of apartness spaces and Bishop-style constructive mathematics. Each of our three criteria can be summarised as requiring that there is a positive distance between any two disjoint closed sets. Neat locatedness and the product apartness give us three variations on this theme. We investigate how our three criteria relate to one another and to several existing compactness criteria, namely classical compactness, completeness, total boundedness, the anti-Specker property, and Diener's neat compactness.

Identiferoai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/5682
Date January 2011
CreatorsSteinke, Thomas Alexander
PublisherUniversity of Canterbury. Mathematics and Statistics
Source SetsUniversity of Canterbury
LanguageEnglish
Detected LanguageEnglish
TypeElectronic thesis or dissertation, Text
RightsCopyright Thomas Alexander Steinke, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml
RelationNZCU

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