Di-uniform texture spaces

Selma Ozcag; Lawrence M. Brown

doi:10.4995/agt.2003.2017

Authors

Selma Ozcag Hacettepe University
Lawrence M. Brown Hacettepe University

DOI:

https://doi.org/10.4995/agt.2003.2017

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

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.

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Author Biographies

Selma Ozcag, Hacettepe University

Department of Mathematics

Lawrence M. Brown, Hacettepe University

Department of Mathematics

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