Strategies in the Banach-Mazur game

WAKE FOREST UNIVERSITY
DEPARTMENT OF MATHEMATICS & STATISTICS

Presents

Lynne Yengulalp
Wake Forest University

Thursday, April 9th, 2020
11am
Virtual Colloquium via Zoom
Meeting details are available via Google Calendar

Abstract: In this talk, I will give an introduction to cardinality of infinite sets including a discussion of countability, uncountability, and the continuum hypothesis. Then I will introduce the Banach-Mazur game. It is a two player game with countably infinitely many rounds played on a subset of R or R^2 (or more generally on a topological space X). The players are named EMPTY and NONEMPTY and they alternate selecting non-empty open subsets, forming a nested sequence. NONEMPTY wins if the intersection of the sequence is non-empty, and EMPTY wins otherwise. Strategies for players in the game (and other topological games) give characterizations of certain notions of completeness. I will discuss some questions related to the existence of strategies for the players. The talk will be accessible to undergraduate students.

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