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Ondřej F. K. Kalenda (2004)
Commentationes Mathematicae Universitatis Carolinae
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We show that a compact space has a dense set of points if it can be covered by countably many Corson countably compact spaces. If these Corson countably compact spaces may be chosen to be dense in , then is even Corson.
Aleksander V. Arhangel'skii, Miroslav Hušek (2008)
Commentationes Mathematicae Universitatis Carolinae
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In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin...
Aleksander V. Arhangel'skii (2013)
Commentationes Mathematicae Universitatis Carolinae
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The class of -spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf -spaces, metrizable spaces with the weight , but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that -spaces are in a duality with Lindelöf -spaces: is an -space if and only if some (every) remainder of in a compactification is a Lindelöf -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math....