Abstract

In this paper, we define compactness for all open sets defined in bi-generalized topological spaces such as: $\mu_{(m,n)}$-semi compactness, $\mu_{(m,n)}$-pre compactness, $\mu_{(m,n)}$-regular compactness, $\mu_{(m,n)}$-$\alpha$-compactness, $\mu_{(m,n)}$-$\beta$-compactness, $\overline{\mu}_{(m,n)}$-compactness and $(m,n)$-compactness. For our investigation, we choose $\mu_{(m,n)}$-semi compactness as a base space and studies the relationships between the $\mu_{(m,n)}$-semi compactness and other compactness in bi-generalized topological spaces.

Keywords and Phrases

Bi-generalized topological spaces, Open sets, Compactness.

A.M.S. subject classification

54A05, 54E55, 54D30.

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