Abstract and Applied Analysis

Topological Quasilinear Spaces

Yılmaz Yılmaz, Sümeyye Çakan, and Şahika Aytekin

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Abstract

We introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. Further, Aseev presented some basic quasilinear counterpart of linear functional analysis by introducing the notions of norm and bounded quasilinear operators and functionals. Our investigations show that translation may destroy the property of being a neighborhood of a set in topological quasilinear spaces in contrast to the situation in topological vector spaces. Thus, we prove that any topological quasilinear space may not satisfy the localization principle of topological vector spaces.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 951374, 10 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495843

Digital Object Identifier
doi:10.1155/2012/951374

Mathematical Reviews number (MathSciNet)
MR2965470

Zentralblatt MATH identifier
1254.46004

Citation

Yılmaz, Yılmaz; Çakan, Sümeyye; Aytekin, Şahika. Topological Quasilinear Spaces. Abstr. Appl. Anal. 2012 (2012), Article ID 951374, 10 pages. doi:10.1155/2012/951374. https://projecteuclid.org/euclid.aaa/1355495843


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