Metric spaces and textures

Senol Dost

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. 


Keywords

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

Subject classification

54E35; 54E40; 18B30; 54E15

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References

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