e^*-Almost Compactness via α-shading

Anjana Bhattacharyya

Department of Mathematics, Victoria Institution (College), 78 B, A.P.C. Road, Kolkata – 700009, India.

Abstract: This paper deals with a new type of compactness viz., α–e^*-almost compactness for crisp subsets of a space X where the underlying structure on X is a fuzzy topology. Several characterizations are made by using ordinary net and power set filterbases as basic tools. It is shown that α–e^*-almost compactness implies α-almost compactness but the converse is true only in α–e^*-regular space.

Keywords: α-e^*–almost compactness, α-e^*–almost compact set, α-e^*–regularity, α^e*–adherent point of net and filterbase, α-e^*–interiorly finite intersection property.

Pages: 163 – 176 | Full PDF Paper