Geodesic
Closed embeddings into complements of $\Sigma$-products
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 4, pp. 647-655

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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 $\Sigma$-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.
Classification : 54B10, 54C25, 54D35, 54D45
Keywords: $\Sigma$-product; Tikhonov cube; Valdivia compact; locally compact space 
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     title = {Closed embeddings into complements of $\Sigma$-products},
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Arhangel'skii, A. V.; Hušek, M. Closed embeddings into complements of $\Sigma$-products. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 4, pp. 647-655. http://geodesic.mathdoc.fr/item/CMUC_2008__49_4_a9/