Special Lecture May 2012

Special lecture by Ostap Chervak on 2012-05-15, 2 - 3 pm (during Professor Friedman's normal lecture time) in the lecture room of the KGRC.

Abstract

Higson corona is a natural object in coarse geometry, being a coarse analogue of Stone-Cech compactification. As a consequence to Parovicenko theorems, I. Protasov proved that under CH Higson coronas of all asymptotically zero-dimensional metric spaces are homeomorphic and wondered if this result remains true in ZFC. We answer negatively on this question and prove that under some set-theoretic assumptions ($\mathfrak u<\mathfrak d$ or MA + OCA) Higson corona of anti-Cantor set is not homeomorphic to Higson corona of divergent sequence $\{n^2\}_{n\in\mathbb{N}}$.