Abstract

In this paper, we shall define the properties for arbitrary topological spaces such as $\alpha_{(\lambda,\lambda')}$-connected spaces and $\mu_{\Omega}$-compact spaces and shall prove the appropriate theorems with counter examples. Also we established that,$\alpha_{(\lambda,\lambda')}$-locally connectedness is an $\alpha_{(\lambda,\lambda')}$-open hereditary and we conclude that $\gamma$-operation defined by Ogata is an restriction of $\lambda$-operation.

Keywords and Phrases

$\alpha_{(\lambda,\lambda')}$-open sets, $\alpha_{(\lambda,\lambda')}$-connected spaces, $\Omega$-open sets, $\mu_{\Omega}$-open sets and $\mu_{\Omega}$-compact spaces.

A.M.S. subject classification

54A05, 54A15, 54B17.

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