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Maximal pseudocompact spaces and the Preiss-Simon property

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Alas O., Tkachuk V., Wilson R.

Open Mathematics

2014

tom 12

nr 3

500-509

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 continuous images while this is not true for the class of countably compact spaces. We prove that every Fréchet-Urysohn compact space is homeomorphic to a retract of a compact MP-space. We also give a ZFC example of a Fréchet-Urysohn compact space which is not maximal pseudocompact. Therefore maximal pseudocompactness is not preserved by continuous images in the class of compact spaces.

Ograniczanie wyników

1 Open Mathematics

1 Alas O.

1 Tkachuk V.

1 Wilson R.

1 2014

Wyniki wyszukiwania

Maximal pseudocompact spaces and the Preiss-Simon property