University of Canterbury Home
    • Admin
    UC Research Repository
    UC Library
    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    1. UC Home
    2. Library
    3. UC Research Repository
    4. Faculty of Engineering | Te Kaupeka Pūhanga
    5. Engineering: Theses and Dissertations
    6. View Item
    1. UC Home
    2.  > 
    3. Library
    4.  > 
    5. UC Research Repository
    6.  > 
    7. Faculty of Engineering | Te Kaupeka Pūhanga
    8.  > 
    9. Engineering: Theses and Dissertations
    10.  > 
    11. View Item

    Constructive Notions of Compactness in Apartness Spaces (2011)

    Thumbnail
    View/Open
    thesis_fulltext.pdf (460.7Kb)
    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
    Collections
    • Engineering: Theses and Dissertations [2903]
    Authors
    Steinke, Thomas Alexander
    show 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

    Related items

    Showing items related by title, author, creator and subject.

    • The circle space of a spherical circle plane 

      Löwen, R.; Steinke, G. F. (BELGIAN MATHEMATICAL SOC TRIOMPHE, 2014)
      We show that the circle space of a spherical circle plane is a punctured projective 3-space. The main ingredient is a partial solution of the problem of Apollonius on common touching circles.
    • New characterisations of tree-based networks and proximity measures 

      Francis A; Semple C; Steel M (2017)
      Phylogenetic networks are a type of directed acyclic graph that represent how a set X of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of ...
    • Projective planes, Laguerre planes and generalized quadrangles that admit large groups of automorphisms 

      Steinke GF (2018)
    Advanced Search

    Browse

    All of the RepositoryCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThesis DisciplineThis CollectionBy Issue DateAuthorsTitlesSubjectsThesis Discipline

    Statistics

    View Usage Statistics
    • SUBMISSIONS
    • Research Outputs
    • UC Theses
    • CONTACTS
    • Send Feedback
    • +64 3 369 3853
    • ucresearchrepository@canterbury.ac.nz
    • ABOUT
    • UC Research Repository Guide
    • Copyright and Disclaimer
    • SUBMISSIONS
    • Research Outputs
    • UC Theses
    • CONTACTS
    • Send Feedback
    • +64 3 369 3853
    • ucresearchrepository@canterbury.ac.nz
    • ABOUT
    • UC Research Repository Guide
    • Copyright and Disclaimer