• ### α-e-Almost Compact Crisp Subsets of a Fuzzy Topological Space

Anjana Bhattacharyya

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

Abstract: Fuzzy e-open set is introduced and studied in [8]. Using this concept as a basic tool, in this paper we introduce α-e-almost compactness for crisp subsets of a topological space by using the concept of α-shading initiated by Gantner et.al [12], a generalized version of fuzzy covering. α-almost compactness is introduced in [13]. Here it is shown that α-e-almost compactness implies α-almost compactness [13], but not conversely. To achieve the converse here we introduce α-e-regular space. We characterize α-e-almost compactness via ordinary net and power set filterbases.

Keywords: Fuzzy e-open set, α-e-almost compact set (space), α-e-regularity, αeadherent point of net and filterbase, α-e-interiorly finite intersection property.