More on $\kappa$-Ohio completeness

Basile, D.. "More on $\kappa $-Ohio completeness." Commentationes Mathematicae Universitatis Carolinae 52.4 (2011): 551-559. <http://eudml.org/doc/246569>.

@article{Basile2011,
abstract = {We study closed subspaces of $\kappa $-Ohio complete spaces and, for $\kappa $ uncountable cardinal, we prove a characterization for them. We then investigate the behaviour of products of $\kappa $-Ohio complete spaces. We prove that, if the cardinal $\kappa ^+$ is endowed with either the order or the discrete topology, the space $(\kappa ^+)^\{\kappa ^+\}$ is not $\kappa $-Ohio complete. As a consequence, we show that, if $\kappa $ is less than the first weakly inaccessible cardinal, then neither the space $\omega ^\{\kappa ^+\}$, nor the space $\mathbb \{R\}^\{\kappa ^+\}$ is $\kappa $-Ohio complete.},
author = {Basile, D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\kappa $-Ohio complete; compactification; subspace; product; -Ohio complete space; closed hereditary property; product space; compactification},
language = {eng},
number = {4},
pages = {551-559},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {More on $\kappa $-Ohio completeness},
url = {http://eudml.org/doc/246569},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Basile, D.
TI - More on $\kappa $-Ohio completeness
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 4
SP - 551
EP - 559
AB - We study closed subspaces of $\kappa $-Ohio complete spaces and, for $\kappa $ uncountable cardinal, we prove a characterization for them. We then investigate the behaviour of products of $\kappa $-Ohio complete spaces. We prove that, if the cardinal $\kappa ^+$ is endowed with either the order or the discrete topology, the space $(\kappa ^+)^{\kappa ^+}$ is not $\kappa $-Ohio complete. As a consequence, we show that, if $\kappa $ is less than the first weakly inaccessible cardinal, then neither the space $\omega ^{\kappa ^+}$, nor the space $\mathbb {R}^{\kappa ^+}$ is $\kappa $-Ohio complete.
LA - eng
KW - $\kappa $-Ohio complete; compactification; subspace; product; -Ohio complete space; closed hereditary property; product space; compactification
UR - http://eudml.org/doc/246569
ER -