Displaying similar documents to “On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces”

A nice class extracted from C p -theory

Vladimir Vladimirovich Tkachuk (2005)

Commentationes Mathematicae Universitatis Carolinae

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We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, ω -stable and ω -monolithic. It is also established that any Sokolov compact space X is Fréchet-Urysohn and the space C p ( X ) is Lindelöf. We prove that any Sokolov space with a G δ -diagonal has a countable network and obtain some cardinality restrictions...

A note on condensations of C p ( X ) onto compacta

Aleksander V. Arhangel'skii, Oleg I. Pavlov (2002)

Commentationes Mathematicae Universitatis Carolinae

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A condensation is a one-to-one continuous mapping onto. It is shown that the space C p ( X ) of real-valued continuous functions on X in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum X (Theorem 19). However, there exists a non-metrizable compactum X such that C p ( X ) condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated.