On the Topological and Uniform Structure of Diversities

Resource type
Date created
2013
Authors/Contributors
Abstract
Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note, we consider the analytical properties of diversities, in particular the generalizations of uniform continuity, uniform convergence, Cauchy sequences, and completeness to diversities. We develop conformities, a diversity analogue of uniform spaces, which abstract these concepts in the metric case. We show that much of the theory of uniform spaces admits a natural analogue in this new structure; for example, conformities can be defined either axiomatically or in terms of uniformly continuous pseudodiversities. Just as diversities can be restricted to metrics, conformities can be restricted to uniformities. We find that these two notions of restriction, which are functors in the appropriate categories, are related by a natural transformation.
Document
Published as
Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 675057, 9 pages
http://dx.doi.org/10.1155/2013/675057
Publication title
Journal of Function Spaces and Applications
Document title
On the Topological and Uniform Structure of Diversities
Date
2013
First page
1
Last page
9
Publisher DOI
10.1155/2013/675057
Copyright statement
Copyright is held by the author(s).
Scholarly level
Peer reviewed?
Yes
Language
Member of collection
Attachment Size
675057.pdf 1.95 MB