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Keywords:
$\Sigma$-product; Tikhonov cube; Valdivia compact; locally compact space
$\Sigma$-product; Tikhonov cube; Valdivia compact; locally compact space
Summary:
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 $\Sigma$-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 axiom and negation of CH, no countable nowhere dense space is a co-Valdivia space.
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