$\mu$-paracompact and $g_\mu$-paracompact generalized topological spaces

Year 2016, Volume: 45 Issue: 2, 447 - 453, 01.04.2016

A. Deb Ray , Rakesh Bhowmick

Abstract

This paper defines generalizations of paracompactness on generalized
topological spaces (GTS) and establishes that paracompactness, near
paracompactness and several other paracompact-like properties follow
as special cases, by choosing the GT suitably. Also, the generalizations
of locally finite and closure preserving collections in a GTS, have been
studied, pointing out their interrelations. Finally, it has been observed
that the celebrated theorem of E.Michael in the context of regular paracompact spaces follow as a corollary to a result achieved in this paper.

Keywords

$\gamma_\mu$-closure, $\mu$-locally finite, $g_\mu$-locally finite, $\mu$-paracompact, $g_\mu$-paracompact, $\gamma_\mu$-regular

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