I-topologies generated by probabilistic norms

被引：0
|
作者：
Zhang, Hua-Peng [1 ]
Wang, Zhen-Ping [2 ]
机构：
[1] Nanjing Univ Posts & Telecommun, Sch Sci, Nanjing 210023, Jiangsu, Peoples R China
[2] Henan Normal Univ, Sch Math & Informat Sci, Xinxiang, Peoples R China
来源：
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS | 2015年 / 28卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Menger probabilistic normed space; I-topological vector space; Q-neighborhood; VECTOR-SPACES; COMPACTNESS;
D O I：
10.3233/IFS-141490
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, an I-topology is constructed in a Menger probabilistic normed space (PNS) in a natural way. Some properties of the I-topology are studied. It is shown that a Menger PNS with the I-topology forms a both locally convex and locally bounded I-topological vector space of QL-type. In addition, the relation between the I-topology and that topologically generated by some classical topologies is investigated.
引用
收藏
页码：2107 / 2111
页数：5
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