Properties of the Space of Group Valued Continuous Functions

Abstract

Abstract—In this paper, we establish necessary and sufficient conditions for countable fan tightness and countable strong fan tightness of the space Cp(T,G) based on Menger property and the Rothberger property, respectively. Additionally, we explore the relationship between countable fan tightness, Reznichenko and Hurewicz properties for the space Cp(T,G). Moreover, we demonstrated that the Menger property is preserved under G equivalence of topological spaces. As a key contribution, we present a general result concerning the fan tightness of Cp(T,G) and the Hurewicz number of the space Tn for every natural number n. Finally, we investigate the monolithicity of the space Cp(T,G).

Publication Title

Iaeng International Journal of Applied Mathematics

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