## Real Analysis Exchange

### The composition of two connected G΄ functions has a fixed point.

Piotr Szuca

#### 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.

#### Article information

Source
Real Anal. Exchange, Volume 29, Number 2 (2003), 931-938.

Dates
First available in Project Euclid: 7 June 2006

https://projecteuclid.org/euclid.rae/1149698566

Mathematical Reviews number (MathSciNet)
MR2083827

Zentralblatt MATH identifier
1068.26004

#### Citation

Szuca, Piotr. The composition of two connected G ΄ functions has a fixed point. Real Anal. Exchange 29 (2003), no. 2, 931--938. https://projecteuclid.org/euclid.rae/1149698566

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