Convergence in graded ditopological texture spaces

Ramazan Ekmekçi, Rıza Ertürk


Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander Sostak (see bibliography). In this paper, the authors generalize the structure of difilters in ditopological texture spaces defined in (see bibliography) to the graded ditopological texture spaces and compare the properties of difilters and graded difilters.


Texture; Graded ditopology; graded difilter; fuzzy topology

Subject classification

54A05; 54A20; 06D10.

Full Text:



L. M. Brown and M. Diker, Ditopological texture spaces and intuitionistic sets, Fuzzy Sets and Systems 98 (1998), 217-224.


L. M. Brown and R. Ertürk, Fuzzy sets as texture spaces, I. Representation theorems, Fuzzy Sets and Systems 110, no. 2 (2000), 227-236.


L. M. Brown, R. Ertürk and S. Dost, Ditopological texture spaces and fuzzy topology, I. Basic concepts, Fuzzy Sets and Systems147, no. 2 (2004), 171-199.


L. M. Brown, R. Ertürk and S. Dost, Ditopological texture spaces and fuzzy topology, II. Topological considerations, Fuzzy Sets and Systems 147, no. 2 (2004), 201-231.


L. M. Brown, R. Ertürk and S. Dost, Ditopological texture spaces and fuzzy topology, III. Separation Axioms, Fuzzy Sets and Systems 157, no. 14 (2006), 1886-1912.


L. M. Brown and A. Sostak, Categories of fuzzy topology in the context of graded ditopologies on textures, Iranian Journal of Fuzzy Systems 11, no. 6 (2014), 1-20.


C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190.


R. Ekmekci and R. Ertürk, Neighborhood structures of graded ditopological texture spaces, Filomat 29, no. 7 (2015), 1445-1459.


R. Ertürk, Separation axioms in fuzzy topology characterized by bitopologies, Fuzzy Sets and Systems 58 (1993), 206-209.


T. Kubiak, On fuzzy topologies, Ph.D. Thesis, A. Mickiewicz University Poznan, Poland, 1985.

S. Özcag, F. Yildiz and L. M. Brown, Convergence of regular difilters and the completeness of di-uniformities, Hacettepe Journal of Mathematics and Statistics 34S (2005), 53-68.

A. Sostak, On a fuzzy topological structure, Rend. Circ. Matem. Palermo, Ser. II, 11 (1985), 89-103.

A. Sostak, Two decades of fuzzy topology: basic ideas, notions and results, Russian Mathematical Surveys 44, no. 6 (1989) 125-186.


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