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The free abelian topological group as a subgroup of the free locally convex topological vector space [PDF]
Journal of Group Theory, 2003 An invariant pseudometric \(\rho\) on an abelian group \(G\) is said to have the Enflo property provided \(\forall_{x\in G}[\rho(x^2,e)=2\rho(x,e)].\) It is proved that a Hausdorff abelian group can be embedded as a topological subgroup in a locally convex Hausdorff topological vector space \(\Leftrightarrow\) the topology of \(G\) is generated by a ...
Carolyn E. McPhail
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Variational inequalities in locally convex Hausdorff topological vector spaces
Archiv der Mathematik, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Verma
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On locally convex I-topological vector spaces
Fuzzy Sets and Systems, 2006 Abstract In this paper, the relation between two definitions of locally convex I -topological vector spaces is studied. These two definitions are introduced by Katsaras [Fuzzy topological vector spaces II, Fuzzy Sets and Systems 12 (1984) 143–154] and Wu and Li [Convexity and fuzzy topological vector spaces, Science Exploration (China) 4(1) (1984) 1–
Hui Zhang, Hui Zhang, Jin-xuan Fang
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Journal of Mathematical Sciences, 2016
For a topological vector space (X, τ), we consider the family LCT(X, τ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ. We prove that for an infinite-dimensional reflexive Banach space (X, τ), the cardinality of LCT(X, τ) is at least \( \mathfrak{c} \).
V. Tarieladze, E. Martín-Peinador
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For a topological vector space (X, τ), we consider the family LCT(X, τ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ. We prove that for an infinite-dimensional reflexive Banach space (X, τ), the cardinality of LCT(X, τ) is at least \( \mathfrak{c} \).
V. Tarieladze, E. Martín-Peinador
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Sequential Separation Theorems and S-Locally Convex Topological Vector Spaces
Mathematische Nachrichten, 1982 The Hahn-Banach theorem, when formulated in a topological vector space, gives rise to a number of 'separation' results. For example: Let (X,t) be a topological vector space (here X is our space, t our topology) over the real or complex field, let A be a non-empty, convex, open subset of X and M an affine subspace of X such that \(A\cap M=\emptyset ...
Ray F. Snipes
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Connectedness of Cone Superefficient Point Sets in Locally Convex Topological Vector Spaces [PDF]
Journal of Optimization Theory and Applications, 2000 For the superefficient point set \(SE(A,K)\) (Borwein/Zhung) in locally convex topological vector spaces it is shown: 1. \(SE(A,K) = \cup_{f \in \operatorname {int} K^*} \{ y \in A: f(y)= \operatorname {inf} \{ f(x): x \in A \} \}\) when \(A\) is \(K\)-convex, 2. \( SE(A,K)\) is connected when \(A\) is \(K\)-convex and weakly compact.
Chen Ling, Y. D. Hu
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Locally Convex Topological Vector Spaces
, 1999 Since convexity will play a central role in all following chapters, the scalar field K over which vector spaces are defined is from now on assumed to be the real field R or the complex field C, unless the contrary is expressly stated. In most definitions and results (for example, the Hahn-Banach theorem) we shall not find it necessary to distinguish ...
M. P. Wolff, H. H. Schaefer
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New definition of locally convex L-topological vector spaces
Fuzzy Sets and Systems, 2009 In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced.
Hua-Peng Zhang, Jin-xuan Fang
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The space of vector‐valued integrable functions under certain locally convex topologies
Mathematische Nachrichten, 2012AbstractLet E be a Banach space, Ω a locally compact space, and μ a positive Radon measure on Ω. In this paper, through extending to Lebesgue‐Bochner spaces, we show that the topology β1 introduced by Singh is a type of strict topology. We then investigate various properties of this locally convex topology.
S. Maghsoudi
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On the Density of Henig Efficient Points in Locally Convex Topological Vector Spaces
Journal of Optimization Theory and Applications, 2014 This paper presents a generalization of the Arrow, Barankin and Blackwell theorem to locally convex Hausdorff topological vector spaces. Our main result relaxes the requirement that the objective set be compact; we show asymptotic compactness is sufficient, provided the asymptotic cone of the objective set can be separated from the ordering cone by a ...
Robert K. Goodrich, Joseph Newhall
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