Abstract
We show that if $f,g\colon[0,1]\to[0,1]$ are both functions with connected $G_\delta$ graphs, then their composition has a fixed point. This is a generalization of the analogous result for Darboux Baire~1 functions.
Citation
Piotr Szuca. "The composition of two connected G΄ functions has a fixed point.." Real Anal. Exchange 29 (2) 931 - 938, 2003-2004.
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