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On the topological category of neutrosophic crisp sets

Year 2023, Volume: 72 Issue: 3, 618 - 632, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1184273

Abstract

In this work, we explicitly characterize local separation axioms as well as generic separation axioms in the topological category of neutrosophic crisp sets, and examine their mutual relationship. Moreover, we characterize several distinct notions of closedness, compactness and connectedness in NCSet, and study their relationship with each other.

References

  • Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1) (1986), 383-395. https://doi.org/10.1016/S0165-0114(86)80034-3
  • Baran, M., Separation properties, Indian J. Pure Appl. Math., 23 (1992), 333-341.
  • Baran, M., The notion of closedness in topological categories, Comment. Math. Univ. Carolin., 34(2) (1993), 383-395.
  • Baran, M., Generalized local separation properties, Indian J. Pure Appl. Math., 25(6) (1994), 615-620.
  • Baran, M., Separation properties in topological categories, Math. Balkanica, 10(1) (1996), 39-48.
  • Baran, M., Altındiş, H., $T_{2}$ objects in topological categories, Acta Math. Hungar., 71(1-2) (1996), 41-48. https://doi.org/10.1007/BF00052193
  • Baran, M., A notion of compactness in topological categories, Publ. Math. Debrecen, 50(3-4) (1997), 221-234.
  • Baran, M., Completely regular objects and normal objects in topological categories, Acta Math. Hungar., 80(3) (1998), 211-224. https://doi.org/10.1023/A:1006550726143
  • Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators, Appl. Categ. Struct., 10(4) (2002), 403-415. https://doi.org/10.1023/A:1016388102703
  • Baran, M., Kula, M., A note on connectedness, Publ. Math. Debr., 68 (2006), 489-501.
  • Baran, M., Separation, connectedness, and disconnectedness, Turk. J. Math., 47(1) (2023), 279-295. https://doi.org/10.55730/1300-0098.3360
  • Baran, T. M., Local $T_{2}$ extended pseudo-quasi-semi metric spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019), 2117-2127. https://doi.org/10.31801/cfsuasmas.497701
  • Baran, T. M., Closedness, separation and connectedness in pseudo-quasi-semi metric spaces, Filomat, 34(14) (2020), 4757-4766. https://doi.org/10.2298/FIL2014757B
  • Baran, T. M., Kula, M., Separation axioms, Urysohn’s lemma and Tietze extention theorem for extended pseudo-quasi-semi metric spaces, Filomat, 36(2) (2022), 703-713. https://doi.org/10.2298/FIL2202703B
  • Bourbaki, N., General Topology, Addison-Wesley Publ. Co., Massachusets, 1966.
  • Dikranjan, D., Giuli, E., Closure operators I, Topol. Appl., 27(2) (1987), 129-143. https://doi.org/10.1016/0166-8641(87)90100-3
  • Herrlich, H., Categorical topology, Gen. Topol. Appl., 1 (1971), 1-15.
  • Hur, K., Lim, P. K., Lee, J. G., Kim, J., The category of neutrosophic crisp sets, Ann. Fuzzy Math. Inform., 14(1) (2017), 43-54.
  • Kula, M., Maraşlı, T., Özkan S., A note on closedness and connectedness in the category of proximity spaces, Filomat, 28(7) (2014), 1483-1492. https://doi.org/10.2298/FIL1407483K
  • Kula, M., Özkan, S., Maraşlı, T., Pre-Hausdorff and Hausdorff proximity spaces, Filomat, 31(12) (2017), 3837-3846. https://doi.org/10.2298/FIL1712837K
  • Kula, M., $ST2, \Delta{T2}, ST3, \Delta{T3}$, Tychonoff, compact and ∂-connected objects in the category of proximity spaces, Hacet. J. Math. Stat., 48(2) (2019), 490-500.
  • Kula, M., Özkan, S., $T_{2}$ and $T_{3}$ objects at p in the category of proximity spaces, Math. Bohem., 145(2) (2020), 177-190. https://doi.org/10.21136/MB.2019.0144-17
  • Marny, T., Rechts-Bikategoriestrukturen in Topologischen Kategorien, Dissertation, Freie Univ., Berlin, 1973.
  • Özkan, S., Alsulami, S., Baran, T. M., Qasim, M., Pre-Hausdorffness and Hausdorffness in quantale-valued gauge spaces, Mathematics, 10(24) (2022), 4819. https://doi.org/10.3390/math10244819
  • Özkan, S., Kula, M., Kula, S., Baran, T. M., Closure operators, irreducibility, Urysohn’s lemma, and Tietze extension theorem for proximity spaces, Turk. J. Math., 47(2) (2023), 870-882. https://doi.org/10.55730/1300-0098.3398
  • Preuss, G., Theory of Topological Structures, An Approach to topological Categories, D. Reidel Publ. Co., Dordrecht, 1988.
  • Qasim, M., Özkan, S., The notion of closedness and D-connectedness in quantalevalued approach spaces. Categ. Gen. Algebr. Struct. Appl., 12(1) (2020), 149-173. https://doi.org/10.29252/CGASA.12.1.149
  • Salama, A. A., Smarandache, F., Neutrosophic Crisp Set Theory, The Educational Publisher, Columbus, Ohio, 2015.
  • Smarandache, F., Neutrosophy: Neutrisophic Property, Sets, and Logic, American Research Press, Rehoboth, USA, 1998.
  • Zadeh, L. A., Fuzzy sets, Inf. Control., 8 (1965), 338-356. https://doi.org/10.1016/S0019-9958(65)90241-X
Year 2023, Volume: 72 Issue: 3, 618 - 632, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1184273

Abstract

References

  • Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1) (1986), 383-395. https://doi.org/10.1016/S0165-0114(86)80034-3
  • Baran, M., Separation properties, Indian J. Pure Appl. Math., 23 (1992), 333-341.
  • Baran, M., The notion of closedness in topological categories, Comment. Math. Univ. Carolin., 34(2) (1993), 383-395.
  • Baran, M., Generalized local separation properties, Indian J. Pure Appl. Math., 25(6) (1994), 615-620.
  • Baran, M., Separation properties in topological categories, Math. Balkanica, 10(1) (1996), 39-48.
  • Baran, M., Altındiş, H., $T_{2}$ objects in topological categories, Acta Math. Hungar., 71(1-2) (1996), 41-48. https://doi.org/10.1007/BF00052193
  • Baran, M., A notion of compactness in topological categories, Publ. Math. Debrecen, 50(3-4) (1997), 221-234.
  • Baran, M., Completely regular objects and normal objects in topological categories, Acta Math. Hungar., 80(3) (1998), 211-224. https://doi.org/10.1023/A:1006550726143
  • Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators, Appl. Categ. Struct., 10(4) (2002), 403-415. https://doi.org/10.1023/A:1016388102703
  • Baran, M., Kula, M., A note on connectedness, Publ. Math. Debr., 68 (2006), 489-501.
  • Baran, M., Separation, connectedness, and disconnectedness, Turk. J. Math., 47(1) (2023), 279-295. https://doi.org/10.55730/1300-0098.3360
  • Baran, T. M., Local $T_{2}$ extended pseudo-quasi-semi metric spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019), 2117-2127. https://doi.org/10.31801/cfsuasmas.497701
  • Baran, T. M., Closedness, separation and connectedness in pseudo-quasi-semi metric spaces, Filomat, 34(14) (2020), 4757-4766. https://doi.org/10.2298/FIL2014757B
  • Baran, T. M., Kula, M., Separation axioms, Urysohn’s lemma and Tietze extention theorem for extended pseudo-quasi-semi metric spaces, Filomat, 36(2) (2022), 703-713. https://doi.org/10.2298/FIL2202703B
  • Bourbaki, N., General Topology, Addison-Wesley Publ. Co., Massachusets, 1966.
  • Dikranjan, D., Giuli, E., Closure operators I, Topol. Appl., 27(2) (1987), 129-143. https://doi.org/10.1016/0166-8641(87)90100-3
  • Herrlich, H., Categorical topology, Gen. Topol. Appl., 1 (1971), 1-15.
  • Hur, K., Lim, P. K., Lee, J. G., Kim, J., The category of neutrosophic crisp sets, Ann. Fuzzy Math. Inform., 14(1) (2017), 43-54.
  • Kula, M., Maraşlı, T., Özkan S., A note on closedness and connectedness in the category of proximity spaces, Filomat, 28(7) (2014), 1483-1492. https://doi.org/10.2298/FIL1407483K
  • Kula, M., Özkan, S., Maraşlı, T., Pre-Hausdorff and Hausdorff proximity spaces, Filomat, 31(12) (2017), 3837-3846. https://doi.org/10.2298/FIL1712837K
  • Kula, M., $ST2, \Delta{T2}, ST3, \Delta{T3}$, Tychonoff, compact and ∂-connected objects in the category of proximity spaces, Hacet. J. Math. Stat., 48(2) (2019), 490-500.
  • Kula, M., Özkan, S., $T_{2}$ and $T_{3}$ objects at p in the category of proximity spaces, Math. Bohem., 145(2) (2020), 177-190. https://doi.org/10.21136/MB.2019.0144-17
  • Marny, T., Rechts-Bikategoriestrukturen in Topologischen Kategorien, Dissertation, Freie Univ., Berlin, 1973.
  • Özkan, S., Alsulami, S., Baran, T. M., Qasim, M., Pre-Hausdorffness and Hausdorffness in quantale-valued gauge spaces, Mathematics, 10(24) (2022), 4819. https://doi.org/10.3390/math10244819
  • Özkan, S., Kula, M., Kula, S., Baran, T. M., Closure operators, irreducibility, Urysohn’s lemma, and Tietze extension theorem for proximity spaces, Turk. J. Math., 47(2) (2023), 870-882. https://doi.org/10.55730/1300-0098.3398
  • Preuss, G., Theory of Topological Structures, An Approach to topological Categories, D. Reidel Publ. Co., Dordrecht, 1988.
  • Qasim, M., Özkan, S., The notion of closedness and D-connectedness in quantalevalued approach spaces. Categ. Gen. Algebr. Struct. Appl., 12(1) (2020), 149-173. https://doi.org/10.29252/CGASA.12.1.149
  • Salama, A. A., Smarandache, F., Neutrosophic Crisp Set Theory, The Educational Publisher, Columbus, Ohio, 2015.
  • Smarandache, F., Neutrosophy: Neutrisophic Property, Sets, and Logic, American Research Press, Rehoboth, USA, 1998.
  • Zadeh, L. A., Fuzzy sets, Inf. Control., 8 (1965), 338-356. https://doi.org/10.1016/S0019-9958(65)90241-X
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Samed Özkan 0000-0003-3063-6168

Publication Date September 30, 2023
Submission Date October 4, 2022
Acceptance Date April 3, 2023
Published in Issue Year 2023 Volume: 72 Issue: 3

Cite

APA Özkan, S. (2023). On the topological category of neutrosophic crisp sets. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(3), 618-632. https://doi.org/10.31801/cfsuasmas.1184273
AMA Özkan S. On the topological category of neutrosophic crisp sets. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. September 2023;72(3):618-632. doi:10.31801/cfsuasmas.1184273
Chicago Özkan, Samed. “On the Topological Category of Neutrosophic Crisp Sets”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 3 (September 2023): 618-32. https://doi.org/10.31801/cfsuasmas.1184273.
EndNote Özkan S (September 1, 2023) On the topological category of neutrosophic crisp sets. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 3 618–632.
IEEE S. Özkan, “On the topological category of neutrosophic crisp sets”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 3, pp. 618–632, 2023, doi: 10.31801/cfsuasmas.1184273.
ISNAD Özkan, Samed. “On the Topological Category of Neutrosophic Crisp Sets”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/3 (September 2023), 618-632. https://doi.org/10.31801/cfsuasmas.1184273.
JAMA Özkan S. On the topological category of neutrosophic crisp sets. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:618–632.
MLA Özkan, Samed. “On the Topological Category of Neutrosophic Crisp Sets”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 3, 2023, pp. 618-32, doi:10.31801/cfsuasmas.1184273.
Vancouver Özkan S. On the topological category of neutrosophic crisp sets. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(3):618-32.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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