Submissions (2)
Accepted (2):
Classification of countably tight groups. — Alex Shibakov <ashibakov@tntech.edu>
We provide a classification of convergence structures in countably tight groups using the Invariant Ideal Axiom and the related Definable Ideal Axiom. We then show some applications to countable groups and the boolean groups with the bounded topology, answering a few published questions. A number of open problems will also be mentioned.
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Equivariant Means and Extension Properties — Natalia Jonard Pérez <nat@ciencias.unam.mx>
An $n$-mean on a topological space $X$ is a symmetric continuous operation $p:X^n\to X$ satisfying $p(x,\dots,x)=x$ for every $x\in X$. The existence of continuous means is closely related to several classical questions in topology, particularly in connection with retract theory and extension properties. In this talk, we discuss equivariant means associated with group actions on topological spaces and their connections with equivariant absolute extensors. Particular attention will be given to involutions (that is, $\mathbb Z_2$-actions) acting on spaces equipped with compatible lattice structures. We will present some existence results and applications in this setting, and explain how they relate to a classical open problem of Anderson. This is a joint work with Ananda López Poo.
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