Forcing countable networks for spaces satisfying $R\left(X^{\omega }\right)=\omega$

Juhász, István, Soukup, Lajos, and Szentmiklóssy, Zoltán. "Forcing countable networks for spaces satisfying $\operatorname{R}(X^\omega )=\omega $." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 159-170. <http://eudml.org/doc/247865>.

@article{Juhász1996,
abstract = {We show that all finite powers of a Hausdorff space $X$ do not contain uncountable weakly separated subspaces iff there is a c.c.c poset $P$ such that in $V^P$$\,X$ is a countable union of $0$-dimensional subspaces of countable weight. We also show that this theorem is sharp in two different senses: (i) we cannot get rid of using generic extensions, (ii) we have to consider all finite powers of $X$.},
author = {Juhász, István, Soukup, Lajos, Szentmiklóssy, Zoltán},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {net weight; weakly separated; Martin's Axiom; forcing; Martin's axiom; weakly separated subset; net weight; forcing},
language = {eng},
number = {1},
pages = {159-170},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Forcing countable networks for spaces satisfying $\operatorname\{R\}(X^\omega )=\omega $},
url = {http://eudml.org/doc/247865},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Juhász, István
AU - Soukup, Lajos
AU - Szentmiklóssy, Zoltán
TI - Forcing countable networks for spaces satisfying $\operatorname{R}(X^\omega )=\omega $
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 159
EP - 170
AB - We show that all finite powers of a Hausdorff space $X$ do not contain uncountable weakly separated subspaces iff there is a c.c.c poset $P$ such that in $V^P$$\,X$ is a countable union of $0$-dimensional subspaces of countable weight. We also show that this theorem is sharp in two different senses: (i) we cannot get rid of using generic extensions, (ii) we have to consider all finite powers of $X$.
LA - eng
KW - net weight; weakly separated; Martin's Axiom; forcing; Martin's axiom; weakly separated subset; net weight; forcing
UR - http://eudml.org/doc/247865
ER -