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Maximal pseudocompact spaces and the Preiss-Simon property

Ofelia Alas, Vladimir Tkachuk, Richard Wilson (2014)

Open Mathematics

We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y. It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant under...

Mazur-like topological linear spaces and their products

Miroslav Hušek (1997)

Commentationes Mathematicae Universitatis Carolinae

Topological linear spaces having the property that some sequentially continuous linear maps on them are continuous, are investigated. It is shown that such properties (and close ones, e.g., bornological-like properties) are closed under large products.

Metrization of function spaces with the Fell topology

Hanbiao Yang (2012)

Commentationes Mathematicae Universitatis Carolinae

For a Tychonoff space X , let C F ( X ) be the family of hypographs of all continuous maps from X to [ 0 , 1 ] endowed with the Fell topology. It is proved that X has a dense separable metrizable locally compact open subset if C F ( X ) is metrizable. Moreover, for a first-countable space X , C F ( X ) is metrizable if and only if X itself is a locally compact separable metrizable space. There exists a Tychonoff space X such that C F ( X ) is metrizable but X is not first-countable.

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