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GRADED DIUNIFORMITIES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 14، شماره 3، شهریور 2017، صفحه 83-103 اصل مقاله (490.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3257 | ||
| نویسندگان | ||
| Ramazan Ekmekci* 1؛ Rza Erturk2 | ||
| 1Department of Mathematics, Canakkale Onsekiz Mart University, Canakkale, TURKEY | ||
| 2Department of Mathematics, Hacettepe University, Ankara, TURKEY | ||
| چکیده | ||
| Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander {\v S}ostak in \cite{BS}. In this paper, the authors generalize the structure of diuniformity in ditopological texture spaces defined in \cite{OB} to the graded ditopological texture spaces and investigate graded ditopologies generated by graded diuniformities. The autors also compare the properties of diuniformities and graded diuniformities. | ||
| کلیدواژهها | ||
| Texture؛ Graded ditopology؛ Graded diuniformity؛ fuzzy topology | ||
| مراجع | ||
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[1] J. Adamek, H. Herrlich and G. E. Strecer, Abstract and concrete categories, New York, Chichester, Brisbane, Toronto, Singapore: John Wiley & Sons, Inc., 1990. [2] L. M. Brown and M. Diker, Ditopological texture spaces and intuitionistic sets, Fuzzy Sets and Systems, 98 (1998), 217{224. [3] L. M. Brown and R. Erturk, Fuzzy sets as texture spaces, I. Representation theorems, Fuzzy Sets and Systems, 110(2) (2000), 227{236. [4] L. M. Brown, R. Erturk and S. Dost, Ditopological texture spaces and fuzzy topology, I. Basic concepts, Fuzzy Sets and Systems, 147(2) (2004), 171{199. [5] L. M. Brown, R. Erturk and S. Dost, Ditopological texture spaces and fuzzy topology, II. Topological considerations, Fuzzy Sets and Systems, 147(2) (2004), 201{231. [6] L. M. Brown, R. Erturk and S. Dost, Ditopological texture spaces and fuzzy topology, III. Separation Axioms, Fuzzy Sets and Systems, 157(14) (2006), 1886{1912. [7] L. M. Brown and A. Sostak, Categories of fuzzy topology in the context of graded ditopologies on textures, Iranian Journal of Fuzzy Systems, 11(6) (2014), 1{20. [8] C. L. Chang, Fuzzy topological spaces, Math. Anal. Appl., 24 (1968), 182{190. [9] R. Ekmekci and R. Erturk, Neighborhood structures of graded ditopological texture spaces, Filomat, 29(7) (2015), 1445{1459. [10] R. Erturk, Separation axioms in fuzzy topology characterized by bitopologies, Fuzzy Sets and Systems, 58 (1993), 206{209. [11] T. Kubiak, On fuzzy topologies, PhD Thesis, A. Mickiewicz University Poznan, Poland (1985). [12] S. Ozcag, Uniform texture spaces, PhD Thesis, Hacettepe University, Ankara, Turkey (2004). [13] S. Ozcag and L. M. Brown, Di-uniform texture spaces, Appiled General Topology, 4(1) (2003), 157{192. [14] S. Ozcag, L. M. Brown and K. Biljana, Di-uniformities and Hutton uniformities, Fuzzy Sets and Systems, 195 (2012), 58{74. [15] S. Ozcag and S. Dost, A categorical view of di-uniform texture spaces, Bol. Soc. Mat. Mexicana, 3(15) (2009), 63{80. [16] A. Sostak, On a fuzzy topological structure, Rend. Circ. Matem. Palermo, Ser. II, 11 (1985), 89{103. [17] A. Sostak, Two decates of fuzzy topology: basic ideas, notions and results, Russian Math. Surveys, 44(6) (1989), 125{186. [18] G. Yldz, Ditopological spaces on texture spaces, MSc Thesis, Hacettepe University, Ankara, Turkey (2005). | ||
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