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Rendiconti del Circolo Matematico di Palermo

, Volume 34, Issue 1, pp 56–78 | Cite as

Pointwise sequential compactness and weak compactness in spaces of contents

  • Hans Weber
Article

Keywords

Compact Subset Weak Topology Weak Measure Weak Compactness Complete Boolean Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Abstract

In questo lavoro si caratterizzano la compattezza sequenziale relativa e la precompattezza sequenziale (a volte detta «conditional compactness») rispetto alla topologia della convergenza puntuale per insiemi di masse aventi condominio separabile. Inoltre usando un teorema di Simons del tipo «〈x′, x n〉→〈x′, x〉, per certix′, implica chex n converge adx debolmente» si ottiene una relazione tra la convergenza puntuale (rispetto alla topologia debole dello spazio dei valori) e la convergenza debole per masse a codominio totalmente limitato. Questi due risultati conducono, generalizzando risultati di Graves/Ruess e Lewis, ad un criterio per la debole compattezza sequenziale relativa e per la debole precompattezza sequenziale di insiemi di masse aventi codominio separabile e totalmente limitato. L’assunzione sugli spazi (localmente convessi) dei valori dipende solo dalla dualità 〈E, E′〉; p.es. E può essere munito sia della topologia debole sia della topologia forte di spazio di Fréchet.

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Copyright information

© Springer 1985

Authors and Affiliations

  • Hans Weber
    • 1
  1. 1.Facoltà di Scienze Matematiche, Fisiche e NaturaliUniversità degli Studi della BasilicataPotenza

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