The theory and applications of generalized H-space. (English) Zbl 0764.54022

Summary: This paper brings forward the concept of generalized \(H\)-spaces which extends the concepts of \(H\)-spaces and almost probabilistic metric spaces. In this paper, the uniformity and properties for generalized \(H\)- spaces are considered. The conditions of metrization and the form of metric functions for generalized \(H\)-spaces, \(H\)-spaces and Menger PM- spaces are given and the characteristics of completeness and compactness for generalized \(H\)-spaces are presented. The results of this paper generalize and unify some recent results of T. L. Hicks and P. L. Sharma [Zb. Rad., Prir.-Mat. Fak., Univ. Novom Sadu, Ser. Mat. 14, No. 1, 35-42 (1984; Zbl 0587.54049)], Zhou Zhongqun [Acta Math. Sin. 29, No. 4, 569-572 (1986), see also the review of Pt. II, ibid. 33, No. 5, 641-645 (1990; Zbl 0712.54019)], B. Schweizer and A. Sklar [Pac. J. Math. 10, 313-334 (1960; Zbl 0091.298) and with E. Thorp, ibid., 673-675 (1960; Zbl 0096.332)].


54E70 Probabilistic metric spaces
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