Forcing countable networks for spaces satisfying R(X^omega)=omega.

Details Forcing countable networks for spaces satisfying R(X^omega)=omega. Forcing countable networks for spaces satisfying R(X^omega)=omega.

1995-03-20

arxiv.org/abs/math/9503208v1

Mathematics

Logic

Scientific paper

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 $X$.

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