New Classes of Generalized PN Spaces and Their Normability

被引：2
作者：
Harikrishnan P.K. [1 ]
Guillén B.L. [2 ]
Cho Y.J. [3 ]
Ravindran K.T. [4 ]
机构：
[1] Department of Mathematics, Manipal Institute of Technology, Manipal University, Manipal, 576104, Karnataka
[2] Departamento de Matemática Aplicada y Estadística, Universidad de Almería, Almería
[3] Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju
[4] Department of Mathematics, Payyanur College, Kannur University, Kannur
来源：
Acta Mathematica Vietnamica | 2017年 / 42卷 / 4期
关键词：
Archimedean; Local convexity; Normability; Probabilistic normed spaces; Topological vector spaces (TVS); Šerstnev spaces;
D O I：
10.1007/s40306-017-0218-z
中图分类号：
学科分类号：
摘要：
In this paper, we obtain some properties of invertible operators; convex, balanced, absorbing sets; and D-boundedness in Šerstnev spaces. We prove that some PN spaces (V,τ∗), which are not Šerstnev spaces, in which the triangle function τ∗ is not Archimedean can be endowed with a structure of a topological vector space, and we give suitable example to illustrate this result. Also, we show that the topological spaces obtained in such a manner are normable under certain given conditions: some examples are given. © 2017, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.
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页码：727 / 746
页数：19
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