Displaying similar documents to “Every weakly initially 𝔪 -compact topological space is 𝔪 pcap”

Open maps do not preserve Whyburn property

Franco Obersnel (2003)

Commentationes Mathematicae Universitatis Carolinae

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We show that a (weakly) Whyburn space X may be mapped continuously via an open map f onto a non (weakly) Whyburn space Y . This fact may happen even between topological groups X and Y , f a homomorphism, X Whyburn and Y not even weakly Whyburn.

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...

Two cardinal inequalities for functionally Hausdorff spaces

Alessandro Fedeli (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the τ θ -closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if X is a functionally Hausdorff space, then | X | ≤ 2 χ ( X ) wcd ( X ) .