![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
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 
. 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 .
Additional information
Notes on contributors
Aleksander Maliszewski
ALEKSANDER MALISZEWSKI received his Ph.D. from the University of Lodz in 1990. He attained the habilitation in mathematics in 1996, also at the University of Lodz. As a teenager, he was a promising chess player. He currently lectures on financial mathematics as an associate professor at Lodz University of Technology.
Marcin Szyszkowski
MARCIN SZYSZKOWSKI obtained his M.Sc. in 1992 at the University of Gdansk and Ph.D. in 2000 at West Virginia University. His favorite pastime is traveling and beer drinking.