Di-uniform texture spaces

Selma Ozcag, Lawrence M. Brown

Abstract

Textures were introduced by the second author as a point-based setting for the study of fuzzy sets, and have since proved to be an appropriate framework for the development of complement-free mathematical concepts. In this paper the authors lay the foundation for a theory of uniformities in a textural context. Analogues are given for both the diagonal and covering approaches to the classical theory of uniform structures, the notion of uniform topology is generalized and an analogue given for the well known result that a topological space is uniformizable if and only if it is completely regular. Finally a textural analogue of the classical interplay between uniformities and families of pseudo-metrics is presented.


Keywords

Uniformity; Texturing; Direlation; Dicover; Difunction; Di-uniform texture space; Uniform ditopology; Uniform bicontinuity; Initial di-uniformity; Separation; Dimetric; Complement-free; Point-free; Fuzzy set

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References

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Cited-By (articles included in Crossref)

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1. Ditopological texture spaces and fuzzy topology, I. Basic concepts
Lawrence M. Brown, Rıza Ertürk, Şenol Dost
Fuzzy Sets and Systems  vol: 147  issue: 2  first page: 171  year: 2004  
doi: 10.1016/j.fss.2004.02.009



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Universitat Politècnica de València

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