T_D Reflexive Spaces
Abstract
In this paper, we characterize strongly open subsets of a reflexive space and show that there is a bijection from the set MB of all strongly open subsets of a reflexive space B onto the set Eq(B) of all equivalence relations on B. Moreover, we characterize each of TD, T1 and T2 reflexive spaces and compare them.
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References
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[2] Adamek, J., Herrlich, H., and Strecker, G.S., Abstract and concrete categories, Wiley, New York, (1990).
[3] Aull, C., Thron, W., Separation axioms between T0 and T1, Indag. math 24, 26–37 (1962).
[4] Baran, M., Separation properties, Indian J. Pure Appl. Math., 23 (5), 333-341, (1991).
[5] Baran, M., The notion of closedness in topological categories, Commentationes Math. Uni. Carolinae, 34 (2), 383-395, (1993).
[6] Baran, M., Al-Safar, J., Quotient-reflective and bireflective subcategories of the category of preordered sets, Topology Appl., 158, 2076-2084, (2011).
[7] Baran, M., Abughalwa, H., Sober spaces, Turkish J. Math, 46, 299-310, (2022).
[8] Baran, M., Stone spaces I, Filomat 38, 5739–5752, (2024).
[9] Baran, M., Separation and compactness in topological categories, Filomat,39 (3), 871-881, (2025).
[10] Baran, M., Topoloji, Second edition, Nobel Akademik Yayıncılık, Ankara, (2025).
[11] Denniston, J.T., Melton, A., Rodabaugh, S.E., Tartir, J.K., A survey and exposition of sub-Hausdorff separation axioms, Quaestiones Mathematicae, 229-285, (2024).
[12] Erciyes, A., Baran, T.M., Separation and connectedness in the category of constant filter convergence spaces, Filomat, 39 (2), 587-600, (2025).
[13] Hoffmann, R.E., On weak Hausdorff spaces, Arch. Math. (Basel), 487-504, (1979).
[14] Larrecq, J.G., Non-Hausdorff topology on domain theory, Cambridge University Press, (2013).
[15] Mielke, M.V., Geometric topological completions with universal final lifts, Topology Appl., 9, 277-293, (1985).
[16] Stine, J., Pre-Hausdorff objects in topological categories, Phd Dissertation, University of Miami, (1997).
[17] Preuss, G., Theory of topological structures, An Approach to topological Categories, D. Reidel Publ. Co., Dordrecht, (1988).
Published
2026-02-16
Section
Special Issue: Advances in Mathematical Sciences
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