ISSN: 1304-7191 | E-ISSN: 1304-7205
The quasicompact-open topology on KC(X,Y)
1Department of Mathematics, Faculty of Arts and Sciences, Nevşehir Hacı Bektaş Veli University, 50300, Nevşehir, Turkey
Sigma J Eng Nat Sci 2023; 41(5): 1070-1075 DOI: 10.14744/sigma.2022.00022
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In this paper, we introduce quasicompact-open topology on 𝐾𝐶(𝑋, 𝑌), the set of all functions from 𝑋 to 𝑌, which are continuous on the compact subsets of 𝑋 and compare this topology with the open-cover topology, the uniform topology and 𝑚-topology. Then, we examine me-trizability, completeness and countability properties of the quasicompact-open topology on 𝐾𝐶(𝑋, 𝑌). Also, we obtain similar results for the open-cover topology and 𝑚- topology on 𝐾𝐶(𝑋, 𝑌).