# Francisco Guevara: Analytic group topologies

Place: Fields Institute (Room 210)

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

Speaker: Francisco Guevera

Title: Analytic group topologies

Abstract: We study the effective version Malykhin’s question about the metrizability of (countable) Frechet groups and its natural generalization to metrizability of (countable) sequential groups of higher sequential order. A countable topological space $(X,\tau)$ is analytic if $\tau$ is analytic as a subset of the Cantor set $2^X$. By effective we mean the group topology is analytic. A space is sequential if all sequentially closed sets are closed. In sequential spaces, the sequential order is defined as the minimal ordinal $\alpha$ so that the closure of every set is obtained by applying the operation of adding limit points $\alpha$-many times. A sequential space has order $1$ iff it is Frechet. The results presented in the talk come from some works of A. Shibakov,  S. Todorcevic, and C. Uzcategui.