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
相关论文
共 50 条
  • [31] Establishing norms with metanorms over interaction topologies
    Mahmoud, Samhar
    Griffiths, Nathan
    Keppens, Jeroen
    Luck, Michael
    AUTONOMOUS AGENTS AND MULTI-AGENT SYSTEMS, 2017, 31 (06) : 1344 - 1376
  • [32] Establishing norms with metanorms over interaction topologies
    Samhar Mahmoud
    Nathan Griffiths
    Jeroen Keppens
    Michael Luck
    Autonomous Agents and Multi-Agent Systems, 2017, 31 : 1344 - 1376
  • [33] Probabilistic norms for linear operators
    Guillen, BL
    Lallena, JAR
    Sempi, C
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 220 (02) : 462 - 476
  • [34] Continuity properties of probabilistic norms
    Alsina, C
    Schweizer, B
    Sklar, A
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 208 (02) : 446 - 452
  • [35] Probabilistic norms on the homeomorphisms of a group
    Alireza Pourmoslemi
    Massimiliano Ferrara
    Bruno Antonio Pansera
    Mehdi Salimi
    Soft Computing, 2020, 24 : 7021 - 7028
  • [36] Probabilistic norms on the homeomorphisms of a group
    Pourmoslemi, Alireza
    Ferrara, Massimiliano
    Pansera, Bruno Antonio
    Salimi, Mehdi
    SOFT COMPUTING, 2020, 24 (10) : 7021 - 7028
  • [37] WDM network topologies - A probabilistic model
    Shekhawat, Virendra Singh
    Tyagi, Dinesh Kumar
    Chaubey, V. K.
    ADCOM 2007: PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON ADVANCED COMPUTING AND COMMUNICATIONS, 2007, : 733 - +
  • [38] Optimized Graph Topologies for Probabilistic Search
    Klaus, Christian
    Chung, Timothy H.
    2011 50TH IEEE CONFERENCE ON DECISION AND CONTROL AND EUROPEAN CONTROL CONFERENCE (CDC-ECC), 2011, : 2913 - 2919
  • [39] TOPOLOGIES AND COTOPOLOGIES GENERATED BY SETS OF FUNCTIONS
    DOW, A
    HENRIKSEN, M
    KOPPERMAN, R
    WOODS, RG
    HOUSTON JOURNAL OF MATHEMATICS, 1993, 19 (04): : 551 - 586
  • [40] TOPOLOGIES GENERATED BY MOISIL RESEMBLANCE RELATIONS
    CALUDE, C
    CAZANESCU, VE
    DISCRETE MATHEMATICS, 1979, 25 (02) : 109 - 115
12345