Smooth embeddings of the Long Line and other non-paracompact manifolds into locally convex spaces [PDF]
arXiv, 2015 We show that every finite dimensional Hausdorff (not necessarily paracompact, not necessarily second countable) $C^r$-manifold can be embedded into a weakly complete vector space, i.e. a locally convex topological vector space of the form ${\mathbb R}^I$ for an uncountable index set $I$ and determine the minimal cardinality of $I$ for which such an ...
arxiv
Lipschitz properties of convex mappings [PDF]
Advances in Operator Theory 2 (2017), no. 1, 21--49, 2016 The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $\Omega$ of a locally convex space $X$ and taking values in a locally convex space $Y$ ordered by a normal cone.
arxiv
"Varopoulos paradigm": Mackey property vs. metrizability in topological groups [PDF]
arXiv, 2016 The class of all locally quasi-convex (lqc) abelian groups contains all locally convex vector spaces (lcs) considered as topological groups. Therefore it is natural to extend classical properties of locally convex spaces to this larger class of abelian topological groups.
arxiv
Cantor's intersection theorem and some generalized fixed point theorems over a locally convex topological vector space [PDF]
, 2020 A. P. Baisnab +2 more
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On Some Topological Concepts of TVS-Cone Metric Spaces and Fixed Point Theory Remarks [PDF]
arXiv, 2011 We prove that every TVS-cone metric space (i.e a cone metric space over a locally convex topological vector space $E$) is first countable paracompact topological space and by using Du's results in " [A note on cone metric fixed point theory and its equivalence, {Nonlinear Analysis},72(5),2259-2261 (2010)]", we conclude that every TVS-cone metric space ...
arxiv
Unitary representability of free abelian topological groups [PDF]
Applied General Topology 9 (2008), No. 2, 197--204, 2006 For every Tikhonov space $X$ the free abelian topological group $A(X)$ and the free locally convex vector space $L(X)$ admit a topologically faithful unitary representation. For compact spaces $X$ this is due to Jorge Galindo.
arxiv
Geometric Structures Induced by Deformations of the Legendre Transform. [PDF]
Entropy (Basel), 2023 Morales PA, Korbel J, Rosas FE.
europepmc +1 more source
arXivThe initial part of this paper is devoted to the notion of pseudo-seminorm on a vector space $E$. We prove that the topology of every topological vector space is defined by a family of pseudo-seminorms (and so, as it is known, it is uniformizable). Then we devote ourselves to the Lipschitz vector structures on $E$, that is those Lipschitz structures on
arxiv
Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces. [PDF]
J Appl Comput Topol, 2023 Lipiński M +3 more
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Fine Properties of Geodesics and Geodesic λ-Convexity for the Hellinger-Kantorovich Distance. [PDF]
Arch Ration Mech Anal, 2023 Liero M, Mielke A, Savaré G.
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