# Francisco Guevara Parra: Analytic spaces and their Tukey types

Place: Fields Institute (Room 210)
Date: March 15, 2018 (13:30-15:00)
Speaker: Francisco Guevara Parra
Title: Analytic spaces and their Tukey types
Abstract: In this Thesis we study topologies on countable sets from the
perspective of Tukey reductions of their neighbourhood
filters. In particular we will study $k$-analytic group topologies
on $\omega$. This will allow us to obtain a metrization theorem
for analytic sequential group topologies on $\omega$, as well
as a classification of such groups in terms of the Tukey type of
the filter of neighbourhoods of the identity. Recall that
a countable topological space is analytic if the topology is analytic
as a subset of the Cantor space.

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