Characterizations of metric completeness

Completeness in Probabilistic Metric Spaces

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Characterizations of Three Types of Completeness

A sequence is complete if every positive integer is a sum of distinct terms of the sequence [1, 3]. In this paper I discuss and characterize this definition and two definitions that generalize it. In Section 1, I give several examples of complete sequences. Section 2 describes how a theorem due to Brown & Weiss [1] can be used to characterize the complete sequences. In Section 3, Weak completen...

Metric Pseudoentropy: Characterizations and Applications

Metric entropy is a computational variant of entropy, often used as a convenient substitute of HILL Entropy, slightly stronger and standard notion for entropy in cryptographic applications. In this paper we develop a general method to characterize metric-type computational variants of entropy, in a way depending only on properties of a chosen class of test functions (adversaries). As a conseque...

ON COMPACTNESS AND G-COMPLETENESS IN FUZZY METRIC SPACES

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

Characterizations of Compactness for Metric Spaces