Local Pre-Hausdorff Constant Filter Convergence Spaces

Year 2018, Volume: 10, 82 - 87, 29.12.2018

Ayhan Erciyes , Mehmet Baran

Abstract

The aim of this paper is to characterize local pre-Hausdorff constant filter convergence spaces and give some invariance properties of them.

Keywords

Topological category, local pre-Hausdorff spaces, constant filter convergence spaces

References

• Adamek, J., Herrlich, H., Strecker, GE., Abstract and Concrete Categories, New York, USA: Wiley, 1990.
• Baran, M., Separation Properties, Indian J. Pure Appl. Math., 23(1991), 333–341.
• Baran, M., Stacks and Filters, Doga-Tr. J. of Mathematics 16(1992), 95–108.
• Baran, M., Separation Properties In Category Of Stack Convergence Spaces, Turkish Journal of Mathematics, 17(1993), 55–62.
• Baran, M., Separation Properties In Categories Of Constant Convergence Spaces, Turkish Journal of Mathematics, 18(1994), 238–248.
• Baran M. and Altindis, H., T2-Objects in Topological Categories, Acta Math. Hungar. 71(1996), 41–48.
• Baran, M., Separation properties in topological categories, Math Balkanica 10(1996), 39–48.
• Baran M., T2-Objects in Categories Of Filter And Local Filter Convergence Spaces, Turkish Journal of Mathematics, 17(1996), 159–168.
• Baran, M., T3 and T4-Objects In Topological Categories, Indian J. Pure Appl. Math., 29(1998), 59–69.
• Baran, M., PreT2 Objects In Topological Categories, Appl. Categor. Struct., 17(2009), 591–602.
• Cartan, H., Filtres et ultrafiltres, CR Acad. Paris, 205(1937), 777–779.
• Cartan, H., Th´eorie des filtres, CR Acad. Paris, 205(1937), 595–598.
• Choquet, G.,Convergences, Ann. Univ. Grenoble Sect. Sci. Math. Phys. (NS) 23.(1948), 57–112.
• Herrlich, H., Topological functors, Gen Topology Appl 4(1974), 125–142.
• Johnstone, P.T., Topos Theory, L.M.S Mathematics Monograph: No. 10. Academic, New York 1977.
• Kowalsky, H.J., Beitrage zur topologischen algebra, Math. Nachrichten 11(1954), 143–185.
• MacLane, S., Moerdijk, I., Sheaves in Geometry and Logic., Springer, New York, 1992.
• Lowen-Colebunders, E., Function Classes of Cauchy Continuous Maps, New York USA; Marcel Dekker Inc, 1989.
• Mielke, M.V., Hausdor_ Separations and Decidability, Symposium on Categorical Topology, University of Cape Town, Rondebosch, (1999), 155–160.
• Nel, L.D., Initially structured categories and cartesian closedness, Canadian J.Math., 27(1975), 1361–1377.
• Preuss, G., Theory of Topological Structures, An Approach to Topological Categories, Dordrecht; D Reidel Publ Co, 1988.
• Royden, H. L., Real Analysis, Macmillan Publishing Co., Inc., 1968.
• Schwarz, F. Hannover, TU., Connections Between Convergence And Nearness, The series Lecture Notes in Mathematics, 719(1979), 345–357.
• Stine, J. Mielke, M.V., Pre-Hausdor_ Spaces, Publ. Math. Debrecen, 73(2008), 379–390.