Paolo Lipparini (2011)
Czechoslovak Mathematical Journal
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The statement in the title solves a problem raised by T. Retta. We also present a variation of the result in terms of -compactness.
Belaid, Karim, Echi, Othman, Lazaar, Sami (2004)
International Journal of Mathematics and Mathematical Sciences
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Witold Marciszewski (1988)
Studia Mathematica
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Luciano Stramaccia (1995)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Paolo Lipparini (2012)
Commentationes Mathematicae Universitatis Carolinae
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We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are shown to be equivalent to a covering property in the sense considered here (Corollary 3.10). Conversely, every covering property is equivalent to the existence of appropriate kinds of accumulation points for arbitrary sequences on some fixed index set...