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Cq(X) Uzayının Sayılabilirlik Özellikleri Üzerine Bazı Sonuçlar

Year 2019, , 582 - 587, 15.07.2019
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
.


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.

Some Results on Countability Properties of C_q (X)

Year 2019, , 582 - 587, 15.07.2019
https://doi.org/10.17714/gumusfenbil.551030

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)
.

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.
There are 21 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

İsmail Osmanoğlu 0000-0002-1005-4075

Publication Date July 15, 2019
Submission Date April 8, 2019
Acceptance Date May 21, 2019
Published in Issue Year 2019

Cite

APA Osmanoğlu, İ. (2019). Cq(X) Uzayının Sayılabilirlik Özellikleri Üzerine Bazı Sonuçlar. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 9(3), 582-587. https://doi.org/10.17714/gumusfenbil.551030