$\mu$-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

References

• Á.Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96(4)(2002), 351 − 357.
• J.Dieudonné, Une généralisation des espaces compacts, J.Math. Pures et. Appl. 23(1944), 65 − 76.
• T.Noiri and B.Roy, Unification of generalized open sets on Topological spaces, Acta Math. Hunger., 130(4)(2011), 349 − 357.
• M.N.Mukherjee and A.Debray, On nearly paracompact spaces via regular even covers, Matematnykn Bechnk, 50(1998), 23 − 29.
• M.K.Singal and S.P.Arya, On nearly paracompact spaces. Matematicˇki Vesnik, 6(21)(1969), 3 − 16.
• R.Shen, Remarks on Products of generalized topology, Acta Math Hunger., 124(4)(2009), 363 − 369.
• N.V.Velicˇko, H-closed topological spaces, Amer. Math. Soc. Transl., 78(2)(1968)103 − 118.