Constructive Notions of Compactness in Apartness Spaces (2011)

View/ Open
Type of Content
Theses / DissertationsThesis Discipline
MathematicsDegree Name
Master of SciencePublisher
University of Canterbury. Mathematics and StatisticsCollections
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; ProximityRights
Copyright Thomas Alexander SteinkeRelated 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 ...