Metric spaces and textures

Senol Dost

Turkey

Hacettepe University

Department of Mathematics and Science Education
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Accepted: 2017-02-15

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Published: 2017-04-03

DOI: https://doi.org/10.4995/agt.2017.6889
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Keywords:

metric space, texture space, uniformity, natural transformation, difunction, isomorphism

Supporting agencies:

This research was not funded

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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