On the reflection of the countable chain condition

Ramiro de la Vega 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
    Universidad de los Andes
    Bogotá, Colombia
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek