# Some properties of the quasicompact-open topology on C(X)

Volume 9, Issue 6, pp 3511--3518 Publication Date: June 05, 2016
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### Authors

Deniz Tokat - Department of Mathematics, Faculty of Arts and Sciences, Nevsehir Hacı Bektas Veli University, 50300 Nevsehir, Turkey. İsmail Osmanoğlu - Department of Mathematics, Faculty of Arts and Sciences, Nevsehir Hacı Bektas Veli University, 50300 Nevsehir, Turkey.

### Abstract

This paper introduces quasicompact-open topology on C(X) and compares this topology with the compact-open topology and the topology of uniform convergence. Then it examines submetrizability, metrizability, separability, and second countability of the quasicompact-open topology on C(X).

### Keywords

• Function space
• set-open topology
• compact-open topology
• quasicompactness
• separability
• submetrizability
• second countability.

•  54C35
•  54D65
•  54E35

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