I. Juhász, L. Soukup, Z. Szentmiklóssy:
Forcing countable networks for spaces satisfying R(X^omega)=omega
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:
-
we can't get rid of
using generic extensions,
- we have to consider all finite powers of X.
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