Local T0 Filter Convergence Spaces

In this paper, we characterize each of local T0 filter convergence spaces and investigate the relationshipsbetween these local T0 filter convergence spaces as well as give some invariance properties of them.

PDF

___

[1] Adamek, J., Herrlich, H., Strecker, G.E., Abstract and Concrete Categories, New York,USA: Wiley, 1990.
[2] Baran, M., Separation properties, Indian J Pure Appl Math 23(1991), 333-341.
[3] Baran, M., Altındis¸, H., T2-Objects in topological categories Acta Math Hungar, 71(1996), 41–48.
[4] Baran, M., Separation properties in topological categories, Math Balkanica 10(1996), 39–48.
[5] Baran, M., Completely regular objects and normal objects in topological categories, Acta Math Hungar 80(1998), 211–224.
[6] Baran, M., T3 and T4 -objects in topological categories, Indian J Pure Appl Math. 29(1998), 59–69.
[7] Baran, M. Kula, S., and Erciyes, A., T0 and T1 semiuniform convergence space, Filomat, 27(2013), 537–546.
[8] Baran, T. M., Local T0 pseudo-quasi-semi metric spaces , Proceedings of 1st International Mediterranean Science and Engineering Congress (IMSEC 2016) C¸ ukurova University, Congress Center, October 26-28, 2016, Adana / TURKEY, 286–291.
[9] Birkhoff, G., A new definition of limit, Bull. Amer. Math. Soc., 41(1935), 636.
[10] Cartan, H., Filtres et ultrafiltres, CR Acad. Paris, 205(1937), 777–779.
[11] Cartan, H., Th´eorie des filtres, CR Acad. Paris, 205(1937), 595–598.
[12] Cook, H.C., and Fisher, H.R., On equicontinuity and continuous convergence, Math. Ann. 159(1965), 94–104.
[13] Gohler, W., ˜ Convergence structures-historical remarks and the monadic approach, Bremen Mathematik Arbeitspapiere, 48(1997), 171–193.
[14] Herrlich, H., Topological functors, Gen Topology Appl 4(1974), 125-142.
[15] Johnstone, PT., Topos Theory, L.M.S Mathematics Monograph: No. 10 New York UAS; Academic Press, 1977.
[16] Kent, D.C., Convergence functions and their related topologies, Fund. Math. 54(1964), 125–133.
[17] Kowalsky, H.J., Beitr˜oge zur topologischen algebra, Math. Nachrichten 11(1954), 143–185.
[18] Kula, M., A note on Cauchy spaces, Acta Math Hungar 133(2011), 14–32.
[19] Lowen-Colebunders, E., Function Classes of Cauchy Continuous Maps, New York USA; Marcel Dekker Inc, 1989.
[20] MacLane, S., Moerdijk I., Sheaves in Geometry and Logic, Springer- Verlag, 1992.
[21] Mielke, M V., Separation axioms and geometric realizations, Indian JPure Appl Math 25(1994), 711–722.
[22] Nel, L.D., Initially structured categories and cartesian closedness, Canadian J.Math., 27(1975), 1361–1377.
[23] Preuss, G., Theory of Topological Structures, An Approach to Topological Categories, Dordrecht; D Reidel Publ Co, 1988.
[24] Schwarz, F., Connections between convergence and nearness, Lecture Notes in Math. Springer-Verlag 719(1978), 345–354.