Metric axioms: a structural study

zbMATH Open1336.54026arXiv1311.0297MaRDI QIDQ3456846

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Publication date: 9 December 2015

Abstract: For a fixed set $X$, an arbitrary extit{weight structure} $din[0,infty{]}^{XimesX}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. extit{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 $[0,infty{]}^{XimesX}$ 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 $X$.

Full work available at URL: https://arxiv.org/abs/1311.0297

zbMATH Keywords

metric spacepseudometric spacequasimetric spacepremetric spacerepresentation of finite lattices

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Representation theory of lattices (06B15)

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