Nonseparable closed vector subspaces of separable topological vector spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00481891" target="_blank" >RIV/67985840:_____/17:00481891 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00605-016-0876-2" target="_blank" >http://dx.doi.org/10.1007/s00605-016-0876-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00605-016-0876-2" target="_blank" >10.1007/s00605-016-0876-2</a>
Alternative languages
Result language
angličtina
Original language name
Nonseparable closed vector subspaces of separable topological vector spaces
Original language description
In 1983 P. Domański investigated the question: For which separable topological vector spaces E, does the separable space [InlineEquation not available: see fulltext.] have a nonseparable closed vector subspace, where c is the cardinality of the continuum? He provided a partial answer, proving that every separable topological vector space whose completion is not q-minimal (in particular, every separable infinite-dimensional Banach space) E has this property. Using a result of S.A. Saxon, we show that for a separable locally convex space (lcs) E, the product space [InlineEquation not available: see fulltext.] has a nonseparable closed vector subspace if and only if E does not have the weak topology. On the other hand, we prove that every metrizable vector subspace of the product of any number of separable Hausdorff lcs is separable.
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/GF16-34860L" target="_blank" >GF16-34860L: Logic and Topology in Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Monatshefte für Mathematik
ISSN
0026-9255
e-ISSN
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Volume of the periodical
182
Issue of the periodical within the volume
1
Country of publishing house
AT - AUSTRIA
Number of pages
9
Pages from-to
39-47
UT code for WoS article
000392032500005
EID of the result in the Scopus database
2-s2.0-84954460567