A.V. Arhangel'skii, M. Hu\v {s}ek
Closed embeddings into complements of $\Sigma $-products

Comment.Math.Univ.Carolin. 49,4 (2008) 647-655.

Abstract: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.

Keywords: $\Sigma $-product, Tikhonov cube, Valdivia compact, locally compact space
AMS Subject Classification: 54B10, 54C25, 54D35, 54D45