Constructive Notions of Compactness in Apartness Spaces (2011)
Type of ContentTheses / Dissertations
Degree NameMaster of Science
PublisherUniversity of Canterbury. Mathematics and Statistics
Steinke, Thomas Alexander
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.
KeywordsConstructive Mathematics; Apartness Spaces; Uniform Spaces; Proximity
RightsCopyright Thomas Alexander Steinke
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