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
  • [41] A NOTE ON TOPOLOGIES GENERATED BY m-STRUCTURES AND omega-TOPOLOGIES
    Al-Omari, Ahmad
    Noiri, Takashi
    COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2018, 67 (01): : 141 - 146
  • [42] Fuzzy topologies generated by fuzzy relations
    Mishra, Seema
    Srivastava, Rekha
    SOFT COMPUTING, 2018, 22 (02) : 373 - 385
  • [43] ON FUZZY TOPOLOGIES GENERATED BY FUZZY RELATIONS
    Mishra, Seema
    Srivastava, Rekha
    TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2021, 11 (03): : 920 - 931
  • [44] Fuzzy topologies generated by fuzzy relations
    Seema Mishra
    Rekha Srivastava
    Soft Computing, 2018, 22 : 373 - 385
  • [45] Topologies on Normed Spaces Generated by Porosity
    Kowalczyk, Stanislaw
    Turowska, Malgorzata
    FILOMAT, 2019, 33 (01) : 335 - 352
  • [46] Preconditioners generated by minimizing norms
    Tarazaga, Pablo
    Cuellar, Diego
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 57 (08) : 1305 - 1312
  • [47] Ordering among the topologies induced by various polynomial norms
    Bernal-Gonzalez, L.
    Cabana-Mendez, H. J.
    Munoz-Fernandez, G. A.
    Seoane-Sepulveda, J. B.
    BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2019, 26 (04) : 481 - 492
  • [48] Some topologies on a Serstnev probabilistic normed space
    Bahrami, Farid
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (02) : 857 - 868
  • [49] Predicative exponentiation of locally compact formal topologies over inductively generated topologies
    Maietti, Maria Emilia
    From Sets and Types to Topology and Analysis: TOWARDS PRACTICABLE FOUNDATIONS FOR CONSTRUCTIVE MATHEMATICS, 2005, 48 : 202 - 222
  • [50] Probabilistic clustering of high dimensional norms
    Naor, Assaf
    PROCEEDINGS OF THE TWENTY-EIGHTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2017, : 690 - 709
12345