Discrete subgroups of normed spaces are free

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00636115" target="_blank" >RIV/67985840:_____/25:00636115 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1112/blms.70051" target="_blank" >https://doi.org/10.1112/blms.70051</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.70051" target="_blank" >10.1112/blms.70051</a>

Result language
angličtina
Original language name
Discrete subgroups of normed spaces are free
Original language description
Ancel, Dobrowolski and Grabowski (Studia Math. 109 (1994): 277–290) proved that every countable discrete subgroup of the additive group of a normed space is free Abelian, hence isomorphic to the direct sum of a certain number of copies of the additive group of the integers. In the present paper, we take a set-theoretic approach based on the theory of elementary submodels and the Singular Compactness Theorem to remove the cardinality constraint from their result and prove that indeed every discrete subgroup of the additive group of a normed space is free Abelian.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-31529X" target="_blank" >GX20-31529X: Abstract convergence schemes and their complexities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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