Reflecting point-countable families

Balogh, Zoltan

doi:10.1090/S0002-9939-02-06621-2

Reflecting point-countable families
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by Zoltan T. Balogh PDF

Proc. Amer. Math. Soc. 131 (2003), 1289-1296 Request permission

Abstract:

It is shown that if every $\leq \omega _{1}$-sized subspace of a (regular) space $X$ of density $\leq \omega _{1}$ has a point-countable base, then so does $X$. Similar results hold for meta-Lindelöfness. Dow’s reflection theorem and a number of other results are deduced as corollaries and applications.

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