Cut points on Brownian paths

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Cut points on Brownian paths

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Title: Cut points on Brownian paths
Author: Burdzy, Krzysztof
Abstract: Let X be a standard two-dimensional Brownian motion. There exists a.s. t [is an element of the set] (0; 1) such that X([0; t))[intersected with] X((t; 1]) = [empty set]. It follows that X([0; 1]) is not homeomorphic to the Sierpinski carpet a.s.

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