# Ian Greig: Dense Subsets of $2^c$ and Independent Families

Place: Fields Institute (Room 210)

Date: September 9th, 2016 (13:30-15:00)

Speaker: Ian Greig

Title: Dense Subsets of $2^c$ and Independent Families

Abstract: We examine the topological space of all functions from the continuum into 2. Specifically, we show that there exists a countable dense subset of this space such that no point in the space is the limit of a sequence from our dense set. Additionally, under the assumption of Martin’s Axiom for Countable Partial Orders, we construct a countable dense subset D such that any discrete subset of D is closed.