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    Constructive Notions of Compactness in Apartness Spaces (2011)

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    Type of Content
    Theses / Dissertations
    UC Permalink
    http://hdl.handle.net/10092/5682
    http://dx.doi.org/10.26021/8345
    
    Thesis Discipline
    Mathematics
    Degree Name
    Master of Science
    Publisher
    University of Canterbury. Mathematics and Statistics
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    • Science: Theses and Dissertations [3784]
    Authors
    Steinke, Thomas Alexandershow all
    Abstract

    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.

    Keywords
    Constructive Mathematics; Apartness Spaces; Uniform Spaces; Proximity
    Rights
    Copyright Thomas Alexander Steinke
    https://canterbury.libguides.com/rights/theses
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