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Metric axioms: a structural study

Weiss, Ittay and Bruno, Jorge (2016) Metric axioms: a structural study. Topology Proceedings , 47 . pp. 59-79. ISSN 0146-4124

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Abstract

For a fixed set X, an arbitrary \textit{weight structure} d∈[0,∞]X×X can be interpreted as a distance assignment between pairs of points on X. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such d naturally arise, such as separation, triangle inequality and symmetry. We present an order-theoretic investigation of various collections of weight structures, as naturally occurring subsets of [0,∞]X×X satisfying certain metric axioms. Furthermore, we exploit the categorical notion of adjunctions when investigating connections between the above collections of weight structures. As a corollary, we present several lattice-embeddability theorems on a well-known collection of weight structures on X.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Technology and Environment (FSTE) > School of Computing, Information and Mathematical Sciences
Depositing User: Ittay Weiss
Date Deposited: 21 Oct 2015 17:49
Last Modified: 21 Oct 2015 17:49
URI: http://repository.usp.ac.fj/id/eprint/8441
UNSPECIFIED

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