Forcing countable networks for spaces satisfying R(X^omega)=omega.
Logic
2016-09-06 v1
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 1_P forces that ``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 can't get rid of using generic extensions, (ii) we have to consider all finite powers of .
Keywords
Cite
@article{arxiv.math/9503208,
title = {Forcing countable networks for spaces satisfying R(X^omega)=omega.},
author = {I. Juhász and Lajos Soukup and Z. Szentmiklóssy},
journal= {arXiv preprint arXiv:math/9503208},
year = {2016}
}