commun. fac. sci. univ. ank. ser. a1 math. stat. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 1303-5991 2618-6470 Ankara University 10.31801/cfsuasmas.1184273 Mathematical Sciences Matematik On the topological category of neutrosophic crisp sets https://orcid.org/0000-0003-3063-6168 Özkan Samed NEVSEHIR HACI BEKTAS VELI UNIVERSITY 09 30 2023 72 3 618 632 10 04 2022 04 03 2023 Copyright © 1948, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 1948 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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.

 Topological category neutrosophic crisp set separation closedness compactness connectedness 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