# Andres Caicedo: Aurichi’s notion of Selective ccc

Day: Monday, November 5
Time: 10:30 am – 11:45 am
Place: MP209

Speaker: Andres Caicedo, Boise State University

Title: Aurichi’s notion of Selective ccc

Abstract: A topological space is separable iff it has a countable dense subset, the reals being a basic example. A weaker condition than separability, but still useful, is the countable chain condition, that a space satisfies iff there are no uncountable sequences of pairwise disjoint non-empty subsets of the space. For example, the topological product of $I$ copies of the discrete space of two elements, $2^I$, is ccc, no matter what the size of $I$ is, but it is not separable if $I$ is larger than the size of the reals.

The study of selection principles, pioneered by Marion Scheepers, plays a significant role in current research in set theoretic topology. Recently, Leandro Aurichi has proposed a definition of a selective version of the countable chain condition. We review some of its basic properties and mention some questions.