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.
| Identifer | oai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/5682 |
| Date | January 2011 |
| Creators | Steinke, Thomas Alexander |
| Publisher | University of Canterbury. Mathematics and Statistics |
| Source Sets | University of Canterbury |
| Language | English |
| Detected Language | English |
| Type | Electronic thesis or dissertation, Text |
| Rights | Copyright Thomas Alexander Steinke, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
| Relation | NZCU |
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