Closed embeddings into complements of $\Sigma$-products

Arhangel'skii, Aleksander V., and Hušek, Miroslav. "Closed embeddings into complements of $\Sigma $-products." Commentationes Mathematicae Universitatis Carolinae 49.4 (2008): 647-655. <http://eudml.org/doc/250483>.

@article{Arhangelskii2008,
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 $-subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin axiom and negation of CH, no countable nowhere dense space is a co-Valdivia space.},
author = {Arhangel'skii, Aleksander V., Hušek, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\Sigma $-product; Tikhonov cube; Valdivia compact; locally compact space; -product; Tikhonov cube; Valdivia compact; locally compact space; co-Valdivia},
language = {eng},
number = {4},
pages = {647-655},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Closed embeddings into complements of $\Sigma $-products},
url = {http://eudml.org/doc/250483},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Arhangel'skii, Aleksander V.
AU - Hušek, Miroslav
TI - Closed embeddings into complements of $\Sigma $-products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 4
SP - 647
EP - 655
AB - 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.
LA - eng
KW - $\Sigma $-product; Tikhonov cube; Valdivia compact; locally compact space; -product; Tikhonov cube; Valdivia compact; locally compact space; co-Valdivia
UR - http://eudml.org/doc/250483
ER -