Di-uniform texture spaces

Selma Ozcag, Lawrence M. Brown


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.


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

Full Text:



L. M. Brown, Relations and functions on textures, preprint.

L. M. Brown and M. Diker, Ditopological texture spaces and intuitionistic sets, Fuzzy Sets and Systems 98 (1998), 217-224. http://dx.doi.org/10.1016/S0165-0114(97)00358-8

L. M. Brown and M. Diker, Paracompactness and full normality in ditopological texture spaces, J. Math. Anal. Appl. 227 (1998), 144-165. http://dx.doi.org/10.1006/jmaa.1998.6090

L. M. Brown and R. Erturk, Fuzzy sets as texture spaces, I. Representation theorems, Fuzzy Sets and Systems 110 (2) (2000), 227-236. http://dx.doi.org/10.1016/S0165-0114(98)00157-2

L. M. Brown and R. Erturk, Fuzzy sets as texture spaces, II. Subtextures and quotient textures, Fuzzy Sets and Systems 110 (2) (2000), 237-245. http://dx.doi.org/10.1016/S0165-0114(98)00158-4

L. M. Brown, R. Erturk and S. Dost, Ditopological texture spaces and fuzzy topology, I. General principles, submitted.

L. M. Brown, R. Erturk and S. Dost, Ditopological texture spaces and fuzzy topology, II. Separation axioms, preprint, 2002.

M. Diker, Connectedness in ditopological texture spaces, Fuzzy Sets and Systems 108 (1999), 223-230. http://dx.doi.org/10.1016/S0165-0114(97)00315-1

G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, A compendium of continuous lattices (Springer-Verlag, Berlin, 1980). http://dx.doi.org/10.1007/978-3-642-67678-9

J. L. Kelley, General Topology (D. Van Nostrand, Princeton, 1955).

G. Sambin, Some points in formal topology, (Proc. Dagstuhl Seminar Topology in Computer Science, June 2000), Theoretical Computer Science, to appear.

J. W. Tukey, Convergence and uniformity in topology, (Ann. of Math. Studies 2, 1940).

A. Weil, Sur les espaces à structure uniforme et sur la topologie générale (Actualités Sci. Ind. 551, Paris, 1937).

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM


Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

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

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt