Cq(X) Uzayının Sayılabilirlik Özellikleri Üzerine Bazı Sonuçlar

Year 2019, Volume: 9 Issue: 3, 582 - 587, 15.07.2019

İsmail Osmanoğlu

https://doi.org/10.17714/gumusfenbil.551030

Abstract

Bu
makalenin amacı C(X) kümesi üzerindeki yarı kompakt-açık topolojinin ikinci
sayılabilirlik, ayrılabilirlik, B0-uzay
özelliği, N0-uzay
özelliği ve kozmik uzay özelliği gibi sayılabilirlik özellikleri için bazı
sonuçlar verilmiştir. Son olarak bu sonuçlar C(X) kümesi üzerindeki
clp-kompakt-açık topoloji için de elde edilmiştir.

Keywords

Fonksiyon uzayı, İkinci Sayılabilirlik, Ayrılabilirlik, P_0-uzayı, ℵ_0-uzayı, Kozmik Uzay

Some Results on Countability Properties of C_q (X)

Abstract

The aim of this
article is to study the countability properties of the quasi compact-open
topology on C (X) such as second
countability, separability and the properties of B0-spaces, N0-spaces and cosmic
spaces. Finally, these results were obtained for clp-compact-open topology on C
(X).

Keywords

Separability, Function space, Second countable, Cosmic Space, P_0-space, ℵ_0-space

References

• Arens, R. F., 1946. A topology for spaces of transformations. Annals of Mathematics, 47, 480–495.
• Arens, R. ve Dugundji, J., 1951. Topologies for function spaces. Pacific Journal of Mathematics, 1, 5–31.
• Banakh, T., 2015. P_0-spaces. Topology and its Applications, 195, 151–173.
• D’Aristotle, A. J., 1973. Quasicompactness and functionally Hausdorff spaces. Journal of the Australian Mathematical Society, 15(3), 319–324.
• Fox, R. H., 1945. On topologies for function spaces. Bulletin of the American Mathematical Society, 51, 429–432.
• Frolik, Z., 1959. Generalization of compact and Lindelöf spaces. Czechoslovak Mathematical Journal, 13(84), 172–217 (Russian).
• Gruenhage, G., 1992. Generalized metric spaces and metrization. s. 239–274. Recent progress in general topology, North-Holland, Amsterdam.
• Gulick, D., 1992. The σ-compact-open topology and its relatives. Mathematica Scandinavica, 30, 159–176.
• Jackson, J. R., 1952. Comparison of topologies on function spaces. Proc. Amer. Math. Soc., 3, 156–158.
• Kundu S. ve McCoy, R.A., 1993. Topologies between compact and uniform convergence on function spaces. Internat. J. Math. Math. Sci., 16, 101–109.
• Kundu, S. ve Garg, P., 2006. The pseudocompact-open topology on C(X). Topology Proceedings, 30(1), 279–299.
• Kundu, S. ve Raha, A. B., 1995. The bounded-open topology and its relatives. Rendiconti dell'Istituto di Matematica dell'Università di Trieste, 27, 61–77.
• McArthur, W. G., 1973. G_δ-diagonals and metrization theorems. Pacific Journal of Mathematics, 44(2), 613-617
• McCoy, R. A. ve Ntantu, I., 1988. Topological Properties of Spaces of Continuous Functions. Springer-Verlag, Berlin.
• Michael, E., 1966. ℵ_0-spaces. J. Math. Mech, 15, 983–1002.
• Ntantu I., 1985. The compact-open topology on C(X), PhD Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, U.S.A.
• Osipov, A. V., 2012. The C-compact-open topology on function spaces. Topology and its Applications, 159, 3059– 3066.
• Osmanoglu, I., 2017. Clp-compact-open topology on function space. Journal of Advanced Studies in Topology, 8(1), 31–39.
• Porter, K. F., 1993. The open-open topology for function spaces. InternationalJournal of Mathematics and Mathematical Sciences, 16 (1), 111–116.
• Sondore, A. ve Sostak, A., 1994. On clp-compact and countably clp-compact spaces. Acta Univ. Latviensis, 595(1994), 123–143.
• Tokat, D. ve Osmanoglu, I., 2016. Some properties of the quasicompact-open topology on C(X). Journal of Nonlinear Sciences and Applications, 9, 3511–3518.