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Level Sets on Disks

Aleksander Maliszewski and Marcin Szyszkowski
The American Mathematical Monthly
Vol. 121, No. 3 (March 2014), pp. 222-228
DOI: 10.4169/amer.math.monthly.121.03.222
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.03.222
Page Count: 7
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Level Sets on Disks
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Abstract

Abstract We prove that every continuous function from a disk to the real line has a level set containing a connected component of diameter at least \documentclass{article} \pagestyle{empty}\begin{document} $\sqrt 3$ \end{document} . We also show that if the disk is split into two sets—one open and the other closed—then one of them contains a component of diameter at least \documentclass{article} \pagestyle{empty}\begin{document} $\sqrt 3$ \end{document} .

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