Compact [formula omitted]-Fuzzy topological spaces

Abstract

Considering complete Boolean algebras G as sets of truth values a new concept of compactness—so-called probabilistic compactness — is introduced to G -fuzzy topological spaces. The aim of this paper is to show that the most important theorems of the theory of ordinary compact spaces remain true; e.g. probabilistic compactness is preserved under projective limits, every probabilistic compact space has an unique G -fuzzy uniformity being compatible with the underlying G -fuzzy topology, etc. Finally using the selection theorem due to Kuratowski and Ryll-Nardzewski a non-trivial example of a probabilistic compact space is given.