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2012 Topological Quasilinear Spaces
Yılmaz Yılmaz, Sümeyye Çakan, Şahika Aytekin
Abstr. Appl. Anal. 2012: 1-10 (2012). DOI: 10.1155/2012/951374


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.


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Yılmaz Yılmaz. Sümeyye Çakan. Şahika Aytekin. "Topological Quasilinear Spaces." Abstr. Appl. Anal. 2012 1 - 10, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1254.46004
MathSciNet: MR2965470
Digital Object Identifier: 10.1155/2012/951374

Rights: Copyright © 2012 Hindawi


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