Exponential domination and its bidual in function spaces

05.10.2021 15:00 - 16:30

V. Tkachuk (Universidad Autónoma Metropolitana; MX)

Given an infinite cardinal \(\kappa\), we say that a space \(X\) features exponential \(\kappa\)-domination if every set \(A \subset X\) with \(|A| \leq 2^\kappa\) is contained in the closure of a set of cardinality \(\leq \kappa\). Evidently, every space \(X\) of density not exceeding \(\kappa\) features exponential \(\kappa\)-domination. We will show that spaces with exponential \(\kappa\)-domination constitute a class with nice categorical properties and, in Cech-complete spaces, exponential \(\kappa\)-domination coincides with density \(\leq \kappa\). Another merit of exponential \(\kappa\)-domination is that it has a bidual in function spaces. To show this, we will introduce exponential \(\kappa\)-cofinality and prove that \(X\) is exponentially \(\kappa\)-cofinal if and only if \(Cp(X)\) features exponential \(\kappa\)-domination and \(X\) is a space with exponential \(\kappa\)-domination if and only if \(Cp(X)\) is exponentially \(\kappa\)-cofinal.

This talk will be given in person.

Please be aware of the fact that you may be required to show proof of your 3G status upon entry of the buildings, or during sporadic random checks in the seminar rooms. During the Logic Colloquium we will also pass around an attendance sheet to facilitate contact tracing. (According to the regulations, this form will be kept for 28 days and destroyed thereafter.)




HS 8, 1. OG, OMP 1