Our standard intuition for abstract topology is geometric: the notion of open set axiomatizes the properties of open balls in metric spaces. Maybe surprisingly, there is an equally applicable, and in some sense formally dual, logical interpretation of topological spaces. In this interpretation, open sets behave like "propositions subject to finite proof." This talk---which assumes no knowledge of mathematical logic---will explore this perspective, in particular as it relates to point-free topology and sheaves.
Graduate Student Geometry-Topology Seminar
Friday, February 7, 2025 - 2:00pm
Riley Shahar
University of Pennsylvania
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