Nonseparable closed vector subspaces of separable topological vector spaces

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Nonseparable closed vector subspaces of separable topological vector spaces

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Nonseparable closed vector subspaces of separable topological vector spaces

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF16-34860L" target="_blank" >GF16-34860L: Logika a topologie v Banachových prostorech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Monatshefte für Mathematik

ISSN

0026-9255

e-ISSN

—

Svazek periodika

182

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

AT - Rakouská republika

Počet stran výsledku

9

Strana od-do

39-47

Kód UT WoS článku

000392032500005

EID výsledku v databázi Scopus

2-s2.0-84954460567