Compact and bounded sets in fuzzy metric spaces (Q2710048)

The authors deal with the structure of the fuzzy metric space (a modified definition of the statistical metric space), which is a triple \((X, M, *)\), where \(X\) is the universe, \(*\) is a triangular norm and \(M:X^2 \times (0, \infty) \to [0,1]\) with properties usual for fuzzy metric spaces. In this space q-bounded, semi-bounded, totally-bounded and unbounded sets are defined. The relation of these sets are studied as well as their relation to the class of F-bounded sets (introduced by the same authors previously). A condition for compactness of \(X\) is formulated in terms of completeness and total boundedness.