# '22

36th Summer Topology Conference

July 18-22, 2022

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

### "The hyperspace of noncut subcontinua of a hairy dendrite"

#### Hernandez-Gutierrez, Rodrigo

For a metric continuum $X$ let $NC^*(X)$ be the set of all subcontinua $Y$ of $X$ such that $X\setminus Y$ is connected, metrized by the Hausdorff metric. I will present the following result obtained jointly with Jorge E. Vega: if $X$ is a dendrite whose set of ramification points is dense, then $NC^*(X)$ is homeomorphic to the Baire space of irrational numbers.

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