TY - JOUR T1 - Cq(X) Uzayının Sayılabilirlik Özellikleri Üzerine Bazı Sonuçlar TT - Some Results on Countability Properties of C_q (X) AU - Osmanoğlu, İsmail PY - 2019 DA - July Y2 - 2019 DO - 10.17714/gumusfenbil.551030 JF - Gümüşhane Üniversitesi Fen Bilimleri Dergisi PB - Gümüşhane Üniversitesi WT - DergiPark SN - 2146-538X SP - 582 EP - 587 VL - 9 IS - 3 LA - tr AB - Bumakalenin amacı C(X) kümesi üzerindeki yarı kompakt-açık topolojinin ikincisayılabilirlik, ayrılabilirlik, B0-uzayözelliği, N0-uzayözelliği ve kozmik uzay özelliği gibi sayılabilirlik özellikleri için bazısonuçlar verilmiştir. Son olarak bu sonuçlar C(X) kümesi üzerindekiclp-kompakt-açık topoloji için de elde edilmiştir. KW - Fonksiyon uzayı KW - İkinci Sayılabilirlik KW - Ayrılabilirlik KW - P_0-uzayı KW - ℵ_0-uzayı KW - Kozmik Uzay N2 - The aim of thisarticle is to study the countability properties of the quasi compact-opentopology on C (X) such as secondcountability, separability and the properties of B0-spaces, N0-spaces and cosmicspaces. Finally, these results were obtained for clp-compact-open topology on C(X). CR - Arens, R. F., 1946. A topology for spaces of transformations. Annals of Mathematics, 47, 480–495. CR - Arens, R. ve Dugundji, J., 1951. Topologies for function spaces. Pacific Journal of Mathematics, 1, 5–31. CR - Banakh, T., 2015. P_0-spaces. Topology and its Applications, 195, 151–173. CR - D’Aristotle, A. J., 1973. Quasicompactness and functionally Hausdorff spaces. Journal of the Australian Mathematical Society, 15(3), 319–324. CR - Fox, R. H., 1945. On topologies for function spaces. Bulletin of the American Mathematical Society, 51, 429–432. CR - Frolik, Z., 1959. Generalization of compact and Lindelöf spaces. Czechoslovak Mathematical Journal, 13(84), 172–217 (Russian). CR - Gruenhage, G., 1992. Generalized metric spaces and metrization. s. 239–274. Recent progress in general topology, North-Holland, Amsterdam. CR - Gulick, D., 1992. The σ-compact-open topology and its relatives. Mathematica Scandinavica, 30, 159–176. CR - Jackson, J. R., 1952. Comparison of topologies on function spaces. Proc. Amer. Math. Soc., 3, 156–158. CR - Kundu S. ve McCoy, R.A., 1993. Topologies between compact and uniform convergence on function spaces. Internat. J. Math. Math. Sci., 16, 101–109. CR - Kundu, S. ve Garg, P., 2006. The pseudocompact-open topology on C(X). Topology Proceedings, 30(1), 279–299. CR - 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. CR - McArthur, W. G., 1973. G_δ-diagonals and metrization theorems. Pacific Journal of Mathematics, 44(2), 613-617 CR - McCoy, R. A. ve Ntantu, I., 1988. Topological Properties of Spaces of Continuous Functions. Springer-Verlag, Berlin. CR - Michael, E., 1966. ℵ_0-spaces. J. Math. Mech, 15, 983–1002. CR - Ntantu I., 1985. The compact-open topology on C(X), PhD Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, U.S.A. CR - Osipov, A. V., 2012. The C-compact-open topology on function spaces. Topology and its Applications, 159, 3059– 3066. CR - Osmanoglu, I., 2017. Clp-compact-open topology on function space. Journal of Advanced Studies in Topology, 8(1), 31–39. CR - Porter, K. F., 1993. The open-open topology for function spaces. InternationalJournal of Mathematics and Mathematical Sciences, 16 (1), 111–116. CR - Sondore, A. ve Sostak, A., 1994. On clp-compact and countably clp-compact spaces. Acta Univ. Latviensis, 595(1994), 123–143. CR - 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. UR - https://doi.org/10.17714/gumusfenbil.551030 L1 - https://dergipark.org.tr/tr/download/article-file/758444 ER -