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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.

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

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.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Memet Kule 0000-0002-2869-2358

Şenol Dost 0000-0002-5762-8056

Publication Date August 1, 2019
Submission Date April 17, 2018
Acceptance Date November 12, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Kule, M., & Dost, Ş. (2019). Texture spaces with ideal. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1596-1610. https://doi.org/10.31801/cfsuasmas.416238
AMA Kule M, Dost Ş. Texture spaces with ideal. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1596-1610. doi:10.31801/cfsuasmas.416238
Chicago Kule, Memet, and Şenol Dost. “Texture Spaces With Ideal”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1596-1610. https://doi.org/10.31801/cfsuasmas.416238.
EndNote Kule M, Dost Ş (August 1, 2019) Texture spaces with ideal. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1596–1610.
IEEE M. Kule and Ş. Dost, “Texture spaces with ideal”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1596–1610, 2019, doi: 10.31801/cfsuasmas.416238.
ISNAD Kule, Memet - Dost, Şenol. “Texture Spaces With Ideal”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1596-1610. https://doi.org/10.31801/cfsuasmas.416238.
JAMA Kule M, Dost Ş. Texture spaces with ideal. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1596–1610.
MLA Kule, Memet and Şenol Dost. “Texture Spaces With Ideal”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1596-10, doi:10.31801/cfsuasmas.416238.
Vancouver Kule M, Dost Ş. Texture spaces with ideal. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1596-610.

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