Free locally convex spaces with a small base
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Free locally convex spaces with a small base
Original language description
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.
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
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales
ISSN
1578-7303
e-ISSN
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Volume of the periodical
111
Issue of the periodical within the volume
2
Country of publishing house
ES - SPAIN
Number of pages
11
Pages from-to
575-585
UT code for WoS article
000396845100019
EID of the result in the Scopus database
2-s2.0-85015383055