The Quasicompact-Open Topology on QC(X)

Year 2019, Volume: 9 Issue: 2, 1090 - 1097, 01.06.2019

İsmail Osmanoğlu

https://doi.org/10.21597/jist.481927

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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