QC(X) Üzerinde Yarı Kompakt-Açık Topoloji

Bu makalede, Tychonoff uzayının yarı kompakt alt kümeleri üzerinde sürekli olan tüm reel değerli fonksiyonların kümesi üzerindeki yarı kompakt-açık topoloji tanıtıldı. Daha sonra bu topolojinin metriklenebilirliği, tam metriklenebilirliği, ayrılabilirliği ve ikinci sayılabilirliği ayrıntılı olarak incelendi.

Anahtar Kelimeler:

Fonksiyon uzayı, Metriklenebilirlik, Tam metriklenebilirlik, Ayrılabilirlik, İkinci sayılabilirlik

The Quasicompact-Open Topology on QC(X)

This paper introduces the quasicompact-open topology on the set of all realvalued functions defined on a Tychonoff space, which are continuous on quasicompact subsets of . Then metrizability, complete metrizability, separability and second countability of this topology are studied in detail.

Keywords:

Function space, Metrizable, Completely metrizable, Separability, Second countable,

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Arens R F, 1946. A topology for spaces of transformations. Annals of Mathematics. 47: 480–495.
Arens R, Dugundji J, 1951. Topologies for function spaces. Pacific Journal of Mathematics. 1: 5–31.
D’Aristotle A J, 1973. Quasicompactness and functionally Hausdorff spaces. Journal of the Australian Mathematical Society. 15(3): 319–324.
Engelking R, 1989. General Topology, revised and completed ed. Heldermann Verlag, Berlin.
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).
Gulick, D, 1992. The σ-compact-open topology and its relatives. Mathematica Scandinavica. 30: 159– 176.
Husain T, 1977. Topology and Maps. Plenum Press, New York.
Jackson J R, 1952. Comparison of topologies on function spaces. Proc. Amer. Math. Soc. 3: 156–158.
Kundu S, Garg P,2016. The pseudocompact-open topology on C(X). Topology Proceedings. 30(1): 279– 299.
Kundu S, 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, Ntantu I, 1988. Topological Properties of Spaces of Continuous Functions. Springer-Verlag, Berlin.
Osipov A V, 2012. The C-compact-open topology on function spaces. Topology and its Applications. 159: 3059–3066.
Porter K F, 1993. The open-open topology for function spaces. InternationalJournal of Mathematics and Mathematical Sciences. 16 (1): 111–116.
Siwiec F,1975. Generalizations of the first axiom of countability. Rocky Mountain J. Math. 5(1): 1-60.
Taylor A. E, Lay D. C, 1980. Introduction to Functional Analysis, 2nd ed.. John Wiley and Sons, New York.
Tokat D, Osmanoglu I, 2016. Some properties of the quasicompact-open topology on C(X). Journal of Nonlinear Sciences and Applications. 9: 3511–3518.