Topological groups with invariant linear spans
Autoři
Rok
2022
Publikováno
Revista Matemática Complutense. 2022, 35(1), 219-226. ISSN 1139-1138.
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Anotace
Given a topological group G that can be embedded as a topological subgroup into some topological vector space (over the field of reals) we say that G has invariant linear span if all linear spans of G under arbitrary embeddings into topological vector spaces are isomorphic as topological vector spaces. For an arbitrary set A let Z(A) be the direct sum of |A|-many copies of the discrete group of integers endowed with the Tychonoff product topology. We show that the topological group Z(A) has invariant linear span. This answers a question from a paper of Dikranjan et al. (J Math Anal Appl 437:1257–1282, 2016) in positive. We prove that given a non-discrete sequential space X, the free abelian topological group A(X) over X is an example of a topological group that embeds into a topological vector space but does not have invariant linear span.
Module-valued functors preserving the covering dimension
Autoři
Rok
2015
Publikováno
Commentationes Mathematicae Universitatis Carolinae. 2015, ISSN 0010-2628.
Productivity of sequences in non-abelian topological groups
Autoři
Rok
2015
Publikováno
Topology and Its Applications. 2015, 163-177. ISSN 0166-8641.
Typ
Článek
Pracoviště
FINITE-VALUED MAPPINGS PRESERVING DIMENSION
Typ
Článek
Pracoviště
Productivity of sequences with respect to a given weight function
Autoři
Spěvák, J.; Shakhmatov, D.; Dikranjan, D.
Rok
2011
Publikováno
Topology and Its Applications. 2011, 2011(158), ISSN 0166-8641.
Group-valued continuous functions with the topology of pointwise convergence
Autoři
Spěvák, J.; Shakhmatov, D.
Rok
2010
Publikováno
Topology and Its Applications. 2010, 2010(157), 1518-1540. ISSN 0166-8641.