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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

  • Czech description

Classification

  • 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

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

  • 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