Di-uniformities and Hutton uniformities

Authors:
Selma Özçağ;Lawrence M. Brown;Biljana Krsteska
Affiliations:
Hacettepe University, Faculty of Science, Mathematics Department, 06800 Beytepe, Ankara, Turkey;Hacettepe University, Faculty of Science, Mathematics Department, 06800 Beytepe, Ankara, Turkey;Sts. Cyril and Methodius University, Faculty of Mathematics and Natural Sciences, 1000 Skopje, Macedonia
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

The authors characterize di-uniformities on a texture (S,S) in the sense of Ozcag and Brown (Di-uniform texture spaces, Appl. Gen. Top. 4(1) (2003), 157-192) in terms of functions on the texturing S. This characterization enables quasi-uniformities in the sense of Hutton (Uniformities on Fuzzy Topological Spaces, J. Math. Anal. Appl. 58 (1977) 559-571) to be regarded as di-uniformities on the corresponding Hutton Texture, thereby revealing di-uniformities as a generalization of Hutton quasi-uniformities. The effect of imposing a complementation on (S,S) is also considered and several important results established.