T_D Reflexive Spaces
DOI :
https://doi.org/10.5269/bspm.81025Résumé
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.
Références
[1] Abughalwa, H., Emir, A., T_D filter convergence spaces, AIP Conf. Proc. 3431, 020001, https://doi.org/10.1063/5.0290243, (2025).
[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).
[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).
Téléchargements
Publié
2026-02-16
Numéro
Rubrique
Conf. Issue: Advances in Mathematical Sciences
Licence
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
