Burdzy, Krzysztof2005-11-172005-11-171989-07Burdzy, K. (1989). Cut points on Brownian paths. Annals of Mathematical Probability 17(3), 1012-1036.http://hdl.handle.net/1773/2162Let 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.247772 bytesapplication/pdfen-USBrownian motioncut pointsfractalrandom fractalArticle