Di-uniform texture spaces


  • Selma Ozcag Hacettepe University
  • Lawrence M. Brown Hacettepe University




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


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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How to Cite

S. Ozcag and L. M. Brown, “Di-uniform texture spaces”, Appl. Gen. Topol., vol. 4, no. 1, pp. 157–192, Apr. 2003.



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