On the reflection of the countable chain condition

2018/04/24 by de la Vega, Ramiro
#54A10 (Secondary) #54A25 #54D30 (Primary) #54G20 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1804.09103

Abstract

We study the question of when an uncountable ccc topological space X contains a ccc subspace of size ℵ₁. We show that it does if X is compact Hausdorff and more generally if X is Hausdorff with pct(X) ≤ ℵ₁. For each regular cardinal κ, an example is constructed of a ccc Tychonoff space of size κ and countable pseudocharacter but with no ccc subspace of size less than κ. We also give a ccc compact T₁ space of size κ with no ccc subspace of size less than κ.

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