Colimits in the category of structural spaces and their realizations in fuzzy-type categories

Document Type : Original Manuscript

Authors

Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

10.22111/ijfs.2026.53824.9550

Abstract

In this paper, we investigate the existence of colimits in the category of O-structural spaces, denoted by OSS. We show that OSS admits all small colimits. Special types of colimits, such as coproducts, coequalizers, and pushouts, are studied in detail. Based on these results, we explicitly describe the ‎O-structures of these colimits in several topological structures that are O‎-structural spaces, including the categories of fuzzy topological spaces in the sense of Chang, intuitionistic fuzzy topological spaces in the sense of Coker, fuzzy topological spaces in the sense of Chakraborty and Ahsanullah, soft and fuzzy soft topological spaces, neutrosophic topological spaces, hypersoft topological spaces and various types of topological molecular lattice structures. In particular, we show how these colimits can be recovered via the underlying O-structural framework. The results shed light on the internal structure of these categories and offer categorical tools for further analysis of generalized topological structures.

Keywords

Main Subjects

References

[1] J. Adámek, H. Herrlich, G. E. Strecker, Abstract and concrete categories, John Wiley and Sons, New York, 1990. Republished in: Reprints in Theory and Applications of Categories, 17, 2006.
[2] M. Akbarpour, G. Mirhosseinkhani, Compactness and closed maps in topological fuzzes, Journal of Mathematical Extension,16(9) (2022), 1-11. https://doi.org/10.30495/JME.2022.1787
[3] N. Çağman, S. Enginoğlu, F. Çıtak, Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems, 8(3) (2011), 137-147. https://doi.org/10.22111/IJFS.2011.292
[4] N. Çağman, S. Karataş, S. Enginoğlu, Soft topology, Computers and Mathematics with Applications, 62(1) (2011), 351-358. https://doi.org/10.1016/j.camwa.2011.05.016
[5] M. K. Chakraborty, T. M. G. Ahsanullah, Fuzzy topology on fuzzy sets and tolerance topology, Fuzzy Sets and Systems, 45(1) (1992), 103-108. https://doi.org/10.1016/0165-0114(92)90096-M
[6] C. L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24(1) (1968), 182-190. https://doi.org/10.1016/0022-247X(68)90057-7
[7] D. Çoker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88(1) (1997), 81-89. https://doi.org/10.1016/S0165-0114(96)00076-0
[8] N. Georgiou, A. C. Megaritis, Soft set theory and topology, Applied General Topology, 15(1) (2014), 93-109. https://doi.org/10.4995/agt.2014.2268
[9] J. A. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1) (1967), 145-174. https://doi.org/10.1016/0022-247X(67)90189-8
[10] J. A. Goguen, The fuzzy tychonoff theorem, Journal of Mathematical Analysis and Applications, 43(3) (1973), 734-742. https://doi.org/10.1016/0022-247X(73)90288-6
[11] S. N. Hosseini, R. Amini, Structural topology in a category, Iranian Journal of Fuzzy Systems, 18(6) (2021), 45-54. https://doi.org/10.22111/IJFS.2021.6332
[12] K. Hur, P. K. Lim, J. G. Lee, J. Kim, The category of neutrosophic sets, Neutrosophic Sets and Systems, 14(1) (2016), 12-20. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1167&context=nss journal
[13] B. Hutton, Products of fuzzy topological spaces, Topology and its Applications, 11(1) (1980), 59-67. https://doi.org/10.1016/0166-8641(80)90017-6
[14] S. Karataş, C. Kuru, Neutrosophic topology, Neutrosophic Sets and Systems, 13 (2016), 90-95. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1160&context=nss journal
[15] M. Z. Kazemi Baneh, S. N. Hosseini, Limits in the category of structural topological spaces, U.P.B. Scientific Bulletin, Series A: Applied Mathematics and Physics, 86(2) (2024), 55-70.
[16] A. Kharal, B. Ahmad, Mappings on fuzzy soft classes, Hindawi Publishing Corporation, Advances in Fuzzy Systems, (2009), 1-6. Article ID 407890. https://doi.org/10.1155/2009/407890
[17] A. Kharal, B. Ahmad, Mappings on soft classes, New Mathematics and Natural Computation, 7(3) (2011), 471-481. https://doi.org/10.1142/S1793005711002025
[18] F. G. Lupiánez, On neutrosophic topology, The International Journal of Systems and Cybernetics, Systems and Management Science, 37(6) (2008), 797-800. https://doi.org/10.1108/03684920810876990
[19] S. Mac Lane, I. Moerdijk, Sheaves in geometry and logic: A first introduction to topos theory, Universitext, Springer-Verlag, New York, 1992. https://doi.org/10.1007/978-1-4612-0927-0
[20] P. K. Maji, A. R. Roy, R. Biswas, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001), 589-602. https://sid.ir/paper/633097/en
[21] Gh. Mirhosseinkhani, N. Nazari, The category of topological De Morgan molecular lattices, Journal of Mathematical Extension, 14(3) (2020), 133-149. https://doi.org/10.30495/jme.v14i0.1127
[22] D. A. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37(4-5) (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
[23] S. Y. Musa, B. A. Asaad, Hypersoft topological spaces, Neutrosophic Sets and Systems, 49 (2022), 397-415. https://doi.org/10.5281/zenodo.6426447
[24] S. E. Rodabaugh, Powerset operator foundations for poslat fuzzy set theories and topologies. In Mathematics of fuzzy sets: logic, topology and measure theory, U. Höhle and S. E. Rodabaugh, eds., The Handbooks of Fuzzy Sets Series, Dordrecht: Kluwer Academic Publishers, 3 (1999), 91-116. https://doi.org/10.1007/978-1-4615-5079-2 3
[25] S. Roy, T. K. Samanta, A note on fuzzy soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2) (2012), 305-311.
[26] M. Saeed, M. Ahsan, A. U. Rahman, A novel approach to mappings on hypersoft classes with application, Theory and Application of Hypersoft Set, (2021), 175-191. https://doi.org/10.5281/zenodo.4743384
[27] M. Saeed, M. Ahsan, M. Siddique, M. Ahmad, A study of the fundamentals of hypersoft set theory, International Journal of Scientific and Engineering Research, 11(1) (2020), 1-9. https://doi.org/10.5281/zenodo.6779593
[28] M. Saeed, A. Rahman, M. Ahsan, F. Smarandache, An inclusive study on fundamentals of hypersoft Set. In Theory and Application of Hypersoft Set, 2021 ed., F. Smarandache, M. Saeed, M. Abdel-Baset, M. Saqlain, Pons Publishing House: Brussels, Belgium, (2021), 1-23. https://doi.org/10.5281/zenodo.7361633
[29] A. A. Salama, S. A. Alblowi, Neutrosophic set and neutrosophic topological spaces, IOSR Journal of Mathematics, 3(4) (2012), 31-35. https://doi.org/10.9790/5728-0343135
[30] A. A. Salama, F. Smarandache, V. Kromov, Neutrosophic closed set and neutrosophic continuous functions, Neu trosophic Sets and Systems, 4(1) (2014), 4-8. https://doi.org/10.5281/zenodo.30213
[31] M. Shabir, M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61(7) (2011), 1786-1799. https://doi.org/10.1016/j.camwa.2011.02.006
[32] F. Smarandache, Extension of soft set to hypersoft set, and then to plithogenic hypersoft set, Neutrosophic Sets and Systems, 22(1) (2018), 168-170.
[33] F. Smarandache, et. al., Proceedings of the first international conference on neutrosophy, neutrosophic logic, neu trosophic set, neutrosophic probability and statistics, University of New Mexico, Gallup, NM 87301, USA (2002). https://doi.org/10.48550/arXiv.math/0306384
[34] B. P. Varol, H. Aygün, Fuzzy soft topology, Hacettepe Journal of Mathematics and Statistics, 41(3) (2012), 407-419. https://izlik.org/JA73DG32JC
[35] G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47(3) (1992), 351-376. https://doi.org/10.1016/0165-0114(92)90301-J
[36] H. Yavari, S. N. Hosseini, Topological molecular lattices as O-structural spaces, 53rd Annual Iranian Mathematics Conference, University of Science and Technology of Mazandaran, (2022), 902-905.
[37] H. Yavari, S. N. Hosseini, Limits in the category of O-structural spaces, 56th Annual Iranian Mathematics Confer ence, Vali-e-Asr University of Rafsanjan, (2025), 335-339.
[38] H. Yavari, S. N. Hosseini, Topologicality, completeness and cocompleteness of the category of structural spaces, Filomat, 40(8) (2026), 2997-3014. https://doi.org/10.2298/FIL2608997Y
Iranian Journal of Fuzzy Systems
Volume 23, Issue 5
September and October 2026
Pages 129-145

Files

Share

How to cite

Statistics