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:

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