Displaying similar documents to “A new kind of compactness for topological spaces”

Topological spaces compact with respect to a set of filters

Paolo Lipparini (2014)

Open Mathematics

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If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and...

A very general covering property

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...

Hausdorff Fréchet closure spaces with maximum topological defect

Riccardo Ghiloni (2002)

Bollettino dell'Unione Matematica Italiana

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It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number ω 1 . In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly ω 1 . Some classical and recent results are deduced from our criterion.