α-Almost Compactness for Crisp Subsets in A Fuzzy Topological Space

摘要

In this paper, using the notion of α-shading of Gantner et al. [6], the idea of α-almost compactness for crisp subsets of a space X is introduced, where the underlying structure on X is a fuzzy topology. Mainly some characterizations of such subsets are incorporated here, which when interpreted for the whole space X, present formulations of an α-almost compact fuzzy topological space. The characterizations include those where ordinary nets and filters are employed as basic tools with the idea of their adherence being defined suitably via the fuzzy topology of the space.