Texture spaces with ideal

Year 2019, Volume: 68 Issue: 2, 1596 - 1610, 01.08.2019

Memet Kule , Şenol Dost

https://doi.org/10.31801/cfsuasmas.416238

Cited By: 1

Abstract

In this paper, the authors define the notion of ideal on texture
spaces. The concept of di-local function is also introduced here by
utilizing the families of neighborhood structure for a ditopological
texture space. These concepts are discussed with a view to finding
new ditopological texture spaces from the original one. Finally, we
introduce and give some properties of weakly bicontinuous
difunction, a subclass of bicontinuous difunction.

Keywords

Ditopology, difunction, di-ideal

References

• Açikgöz, A., Noiri, T. and Yüksel, Ş., A Decomposition of Continuity in Ideal Topological Spaces, Acta Math. Hungar., 105, No. 4 (2004) 285-289.
• Aslim, G., Caksu Güler, A. and Noiri, T., On decompositions of continuity and some weaker forms of continuity via idealization, Acta Math. Hungar., 109, No. 3 (2005) 183--190.
• Brown, L. M. and Ertürk, R., Fuzzy Sets as Texture Spaces, I. Representation Theorems, Fuzzy Sets and Systems, 110, No. 2 (2000) 227--236.
• Brown, L. M. and Diker, M., Ditopological texture spaces and intuitionistic sets, Fuzzy Sets and Systems, 98 (1998) 217--224.
• Brown, L. M., Ertürk, R. and Dost, Ş., Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147, No. 2 (2004) 171--199.
• Brown, L. M., Ertürk, R. and Dost, Ş., Ditopological texture spaces and fuzzy topology, II. Topological Considerations, Fuzzy Sets and Systems 147, No. 2 (2004) 201--231.
• Brown, L. M., Ertürk, R. and Dost, Ş., Ditopological texture spaces and fuzzy topology, III. Separation Axioms, Fuzzy Sets and Systems 157, No. 14 (2006) 1886--1912.
• Diker, M., Textural approach to rough sets based on relations, Inf. Sci. 180, No. 8 (2010) 1418--1433 .
• Dost, Ş., A textural view of soft fuzzy rough sets, Journal of Intelligent Fuzzy Systems 28 (2015), 2519-2535.
• Ekici, E. and Noiri, T., Connectedness in ideal topological spaces, Novi Sad Journal of Mathematics 38, No. 2 (2008) 65--70.
• Hamlett, T.R. and Jankovic, D., Compactness with respect to an ideal, Boll. U.M.I. 7, No. 4-B (1990) 849-862.
• Hayashi, E., Topologies defined by local properties, Math. Ann., 156 (1964) 205-215.
• Newcomb, R.L., Topologies which are compact modulo an ideal, Ph.D. Thesis, Uni. of Cal. at Santa Barbara, 1967.
• Jankovic, D. and Hamlett, T.R., New topologies from old via ideals, Amer. Math. Monthly, 97 (1990) 295-310.
• Kule, M. and Dost, Ş., A textural view of semi-separation axioms in soft fuzzy topological spaces, Journal of Intelligent Fuzzy Systems, 30 (2016) 2037-2053.
• Kuratowski, K., Topology, Vol. I, Academic Press, New York, 1966.
• Levine, N., A decomposition of continuity in topological spaces, Amer. Math. Monthly, 68 (1961) 44--46.
• Özcağ, S., Yıldız, F. and Brown, L. M., Convergence of regular difilters and the completeness of di-uniformities, HJMS, 34, S (Doğan Çoker Memorial Issue) (2005) 53--68.
• Rancin, D.V., Compactness modulo an ideal, Soviet Math. Dokl., 13, No. 1 (1972) 193-197.
• Samuels, P., A topology formed from a given topology and ideal, J. London Math. Soc., 10 (1975) 409-416.
• Vaidyanathaswamy, R., Set Topology, Chelsea Publishing Company, 1960.