Metric spaces and textures
Submitted: 2016-11-20
|Accepted: 2017-02-15
|Published: 2017-04-03
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Keywords:
metric space, texture space, uniformity, natural transformation, difunction, isomorphism
Supporting agencies:
Abstract:
Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. Further dimetric on textures is a gener- alization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical approach. We prove that the category of clas- sical metric spaces is isomorphic to a full subcategory of dimetric texture spaces, and give a natural transformation from metric topologies to dimetric ditopologies. Further, it is pre- sented a relation between dimetric texture spaces and quasi-pseudo metric spaces in the sense of J. F. Kelly.
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