α-fuzzy compactness in I-topological spaces

Abstract

Using a gradation of openness in a (Chang fuzzy) I -topological space, we introduce degrees of compactness that we call α -fuzzy compactness (where α belongs to the unit interval), so extending the concept of compactness due to C. L. Chang. We obtain a Baire category theorem for α -locally compact spaces and construct a one-point α -fuzzy compactification of an I -topological space.