Selma Özçağ

Di-uniformities and Hutton uniformities

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.

The concept of quasi-uniformity in texture space and its representation

Abstract In this paper the author lays the foundation for a theory of quasi-di-uniformities on textures, giving descriptions in terms of direlations, dual dicovers and quasi-pseudo dimetrics. The category of quasi-di-uniformities and uniformly bicontinuous difunctions is also introduced.

Weaker forms of the Menger property in bitopological spaces

Abstract In this paper we continue previous investigations on the weaker forms of the Menger property in bitopological spaces. We introduce weakly Menger property and study some topological properties of almost and weakly Menger bitopological spaces. We also consider the almost Hurewicz spaces in a bitopological context.