Constructive Notions of Compactness in Apartness Spaces

MSc Thesis - University of Canterbury

Thomas Steinke

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.

Supervisor: Douglas Bridges
Thesis: [University of Canterbury Library] [pdf]
Presented at: CCA 2011 (Slides: [pdf])
   author = {Thomas Steinke},
   title = {Constructive Notions of Compactness in Apartness Spaces},
   school = {University of Canterbury},
   year = {2011},
   url = {},

Last updated on 1 March 2012 by Thomas Steinke.