Free locally convex spaces with a small base
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00474089" target="_blank" >RIV/67985840:_____/17:00474089 - isvavai.cz</a>
Výsledek na webu
<a href="http://dx.doi.org/10.1007/s13398-016-0315-1" target="_blank" >http://dx.doi.org/10.1007/s13398-016-0315-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-016-0315-1" target="_blank" >10.1007/s13398-016-0315-1</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Free locally convex spaces with a small base
Popis výsledku v původním jazyce
The paper studies the free locally convex space L(X) over a Tychonoff space X. Since for infinite X the space L(X) is never metrizable (even not Fréchet-Urysohn), a possible applicable generalized metric property for L(X) is welcome. We propose a concept (essentially weaker than first-countability) which is known under the name a G-base. A space X has a G-base if for every x in X there is a base { Ualpha: alpha in NN} of neighborhoods at x such that Ubeta ... Ualpha whenever alpha ... beta for all alpha, beta in NN, where alpha = (alpha(n)) n in N... N. We show that if X is an Ascoli omega-compact space, then L(X) has a G-base if and only if X admits an Ascoli uniformity U with a G-base. We prove that if X is a omega-compact Ascoli space of NN-uniformly compact type, then L(X) has a G-base. As an application we show: (1) if X is a metrizable space, then L(X) has a G-base if and only if X is omega-compact, and (2) if X is a countable Ascoli space, then L(X) has a G-base if and only if X has a G-base.
Název v anglickém jazyce
Free locally convex spaces with a small base
Popis výsledku anglicky
The paper studies the free locally convex space L(X) over a Tychonoff space X. Since for infinite X the space L(X) is never metrizable (even not Fréchet-Urysohn), a possible applicable generalized metric property for L(X) is welcome. We propose a concept (essentially weaker than first-countability) which is known under the name a G-base. A space X has a G-base if for every x in X there is a base { Ualpha: alpha in NN} of neighborhoods at x such that Ubeta ... Ualpha whenever alpha ... beta for all alpha, beta in NN, where alpha = (alpha(n)) n in N... N. We show that if X is an Ascoli omega-compact space, then L(X) has a G-base if and only if X admits an Ascoli uniformity U with a G-base. We prove that if X is a omega-compact Ascoli space of NN-uniformly compact type, then L(X) has a G-base. As an application we show: (1) if X is a metrizable space, then L(X) has a G-base if and only if X is omega-compact, and (2) if X is a countable Ascoli space, then L(X) has a G-base if and only if X has a G-base.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
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)
Ostatní
Rok uplatnění
2017
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales
ISSN
1578-7303
e-ISSN
—
Svazek periodika
111
Číslo periodika v rámci svazku
2
Stát vydavatele periodika
ES - Španělské království
Počet stran výsledku
11
Strana od-do
575-585
Kód UT WoS článku
000396845100019
EID výsledku v databázi Scopus
2-s2.0-85015383055