The Quasicompact-Open Topology on QC(X)

Abstract

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

QC(X) Üzerinde Yarı Kompakt-Açık Topoloji

Abstract

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.

Keywords

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

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