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

1995/03/20 by I. Juhász, Juhász, I., Lajos Soukup +3
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/9503208

arxiv created 1995/03/20 · arxiv updated 2016/09/06

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 X.

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