# Tomasz Żuchowski: Nonseparable growth of omega supporting a strictly positive measure

Tuesday, March 15, 2016, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Tomasz Żuchowski (University of Wroclaw)

Title: Nonseparable growth of $\omega$ supporting a strictly positive measure

Abstract:

We will construct in ZFC a compactification $\gamma\omega$ of
$omega$ such that its remainder $\gamma\omega\backslash\omega$ is not
separable and carries a strictly positive measure, i.e. measure positive
on nonempty open subsets. Moreover, the measure on our space is defined by
the asymptotic density of subsets of $\omega$.

Our remainder is a Stone space of a Boolean subalgebra of Lebesgue
measurable subsets of $2^{\omega}$ containing all clopen sets.