Topological Quasilinear Spaces
Küçük Resim Yok
Tarih
2012
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Hindawi Publishing Corporation
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Convex-Bodies
Kaynak
Abstract and Applied Analysis
WoS Q Değeri
Q1
Scopus Q Değeri
Q4
