# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Topological characterizations of the n-dimensional Sierpinski Carpet"

#### Rocha de Souza, Lucas Henrique

Whyburn showed that if we take a 2-sphere and remove an infinite collection of open disks satisfying some properties, then we get the 1-dimensional Sierpinski carpet. After that, Cannon generalized it for n-dimensional Sierpinski Carpets, with n different than 3. Recently, Tshishiku and Walsh gave another characterization of the Sierpinski Carpet: if we take a 2-sphere, remove a countable dense set and replace each point by a circle, then we get a 1-dimensional Sierpinski Carpet. We generalized their result for a n-dimensional Sierpinski Carpet, with n different than 3.

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