Compactness in the endograph uniformity

Abstract

Given a uniform space (X,U), we denote by F*(X) to the family of fuzzy sets u in (X,U) such that u is normal and upper semicontinuous. Let UE be the endograph uniformity on F*(X). In this paper, we mainly characterize totally bounded and compact substes in the uniform space (F*(X),UE).

Keywords

• fuzzy sets
• endograph uniformity
• endograph metric
• sendograph uniformity
• sendograph metric
• completeness
• compactness