Stuart Nygard: The density topology

Wednesday, April 29 from 3 to 4pm
Room: Math 124
Speaker: Stuart Nygard (BSU)
Title: The density topology

Abstract: In the Euclidean topology, open sets are defined by unions of open intervals. Can we remove some “small” set from the intervals and still have a meaningful topology? Yes. We define a topology using sets that have locally full measure. That is, a set will have an open neighborhood around a point if “almost every” point nearby belongs to the set. We will show how the topology naturally arises on R and other spaces. No knowledge of Lebesgue measure or topology is assumed.

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