广义H-空间的理论及其应用*
The Theory and Applications of Generalized H-Space
-
摘要: 本文给出了广义H-空间的完备性特征性质和紧性特征性质,同时也研究了这一空间的度量化定理.作为这些理论的应用.我们得到了Menger概率度量空间的完备性特征和紧性特征.给出了该空间的度量化函数的具体形式.Abstract: 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 far generalized H-space 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 [1-2, 8, 10].
-
Key words:
- uniform spaces /
- H-spaces /
- probabilistic metric spaces /
- metrization
-
[1] Hicks T.L.and P.L.Sharm,Probabilistic metric structures;topological classitication. [2] Zhornik Radova Prirodno-Matematickog Fakultetu a Novom Sadu, Serija za Matemutiku, 14(1984), 35-42. [3] 周忠群,几乎概率度量空间,数学学报,29(4)(1986), 569-572. [4] 张石生,《不动点理论及其应用》,重庆出版社(1984). [5] 张石生.概率度量空间中映象的不动点定理及其应用,中国科学,A辑,6 (1983), 495-504 [6] Scweizer B.and A.Sklar,Probabilistic Metric Spaces.North-Holland(1983). [7] Engelking R.General Topology.Warszawa(1977). [8] Menger K Statistical metrics,Proc Nat Acad of Sci U.S.A.28(1942).535-537 [9] Schweizer,B.and A.Sklar,Statistical metric spaces.Pacific J.Math 10(1960).313-334. [10] 游兆永、朱林户,科学通报,(8)(1983). [11] Schweizer B.A.Sklar and T.Thorp.he metrization of statistical metric spaces.Pacific J.Math.10(1960).673-675. [12] Hicks.T.L.Fixed point theory in probabilistic metric spaces.Zbornik radova Prirodno-Matematickog Fakulteta u Novom Sadu.Serija za Matematiku.13(1983).63-72 [13] Chang Shin-sen,The metrization of probabilistic metric spaccs with applications,Zbornik Radowa Privodno-Matematickong Fakuherta u Novom Sadu.Serija za Matemariku,15(1)(1985).107-117. [14] 张石生、车素兵,概率度量空间的度量化及不动点,数学季刊.(2) (1987), 54-60 [15] Sehgal.V.M.and A.T.Bharucha-Reid.Math.Systems.Theory.6(2)(1972),97-102． -
点击查看大图
计量
- 文章访问数: 2133
- HTML全文浏览量: 95
- PDF下载量: 502
- 被引次数: 0
下载:
