I-topologies generated by probabilistic norms1

Article type: Research Article

Authors: Zhang, Hua-Peng^{a; *} | Wang, Zhen-Ping^b

Affiliations: [a] School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China | [b] School of Mathematics and Information Science, Henan Normal University, Xinxiang, China

Correspondence: [*] Corresponding author: Hua-Peng Zhang, School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China. Tel.: +86 2585866608; Fax: +86 2585866600;E-mail: huapengzhang@163.com

Note: [1] Supported by the National Natural Science Foundation of China (No. 11301281) and 1311 Talent Program of NJUPT.

Abstract: 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.

DOI: 10.3233/IFS-141490

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 5, pp. 2107-2111, 2015