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On the reflection of the countable chain condition

Fundamenta Mathematicae MSC: Primary 54A25, 54G20, 54D30; Secondary 54A10. DOI: 10.4064/fm671-12-2018 Opublikowany online: 7 June 2019

Streszczenie

We study the question of when an uncountable ccc topological space $X$ contains a ccc subspace of size $\aleph _1$. We show that it does if $X$ is compact Hausdorff and more generally if $X$ is Hausdorff with $\mathrm {pct}(X) \leq \aleph _1$. For each regular cardinal $\kappa$, an example is constructed of a ccc Tikhonov space of size $\kappa$ and countable pseudocharacter but with no uncountable ccc subspace of size less than $\kappa$. We also give a ccc compact $T_1$ space of size $\kappa$ with no uncountable ccc subspace of size less than $\kappa$.

Autorzy

• Ramiro de la VegaDepartamento de Matemáticas