Abstract

In this paper we introduce the concepts $ \mathcal{G} $ - locally finite, $ \sigma_{\mathcal{G}} $ - locally finite and $ \mathcal{G} $ - paracompactness. Also discuss about some properties of these concepts. Here we investigate that some properties in topological spaces and generalized topological spaces (GTS) are coincides if we replace open sets by generalized open sets ($ \mathcal{G} $ - open sets ). Also, we provide some examples to show some results are invalid in the case of GTS.

Keywords and Phrases

$\mathcal{G}$ - locally finite, $\sigma_{\mathcal{G}}$ - locally finite, $\mathcal{G}$ - paracompactness.

A.M.S. subject classification

22A99.

.....