Topological groups with invariant linear spans
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F22%3A00351185" target="_blank" >RIV/68407700:21240/22:00351185 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13163-020-00383-7" target="_blank" >https://doi.org/10.1007/s13163-020-00383-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13163-020-00383-7" target="_blank" >10.1007/s13163-020-00383-7</a>
Alternative languages
Result language
angličtina
Original language name
Topological groups with invariant linear spans
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ18-00960Y" target="_blank" >GJ18-00960Y: Selected topics in non-linear functional analysis and approximation theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista Matemática Complutense
ISSN
1139-1138
e-ISSN
1988-2807
Volume of the periodical
35
Issue of the periodical within the volume
1
Country of publishing house
IT - ITALY
Number of pages
8
Pages from-to
219-226
UT code for WoS article
000608636700001
EID of the result in the Scopus database
2-s2.0-85100013602