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On Local Quasi-Convexity as a Three-Space Property in Topological Abelian Groups
(Elsevier, 2021)
[Abstract] Let X be a topological abelian group and H a subgroup of X. We find conditions under which local quasi-convexity of both H and results in the same property for X. This is true for instance if H is precompact, ...
Topological Groups of Lipschitz Functions and Graev Metrics
(Elsevier, 2022)
[Abstract] We study the properties of the free abelian topological group Ad(X) on a metric space (X,d) endowed with the topology generated by the Graev extension dˆ of a given metric d on X. We find that the group of ...
Krein’s theorem in the context of topological abelian groups
(MDPI, 2022)
[Abstract:] A topological abelian group G is said to have the quasi-convex compactness property (briefly, qcp) if the quasi-convex hull of every compact subset of G is again compact. In this paper we prove that there exist ...
Permutations, Signs, and Sum Ranges
(MDPI, 2023)
[Abstract:] The sum range SR[x; X], for a sequence x = (xn)n∈N of elements of a topological vector space X, is defined as the set of all elements s ∈ X for which there exists a bijection (=permutation) π : N → N, such that ...
On the existence of topologies compatible with a group duality with predetermined properties
(Elsevier, 2022)
[Abstract:] The paper deals with group dualities. A group duality is simply a pair (G, H) where G is an abstract abelian group and H a subgroup of characters defined on G. A group topology τ defined on G is compatible with ...
On g-barrelled groups and their permanence properties
(Elsevier, 2019)
[Abstract:] The g-barrelled groups constitute a vast class of abelian topological groups. It might be considered as a natural extension of the class of barrelled topological vector spaces. In this paper we prove that ...
On local cross sections in topological abelian groups
(Springer, 2018)
[Abstract:] We introduce the notion of local pseudo-homomorphism between two topological abelian groups. We prove that it is closely related with the widely studied notions of local cross sections and splitting extensions ...