# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Sharkovskiĭ's theorem holds for some discontinuous functions

### Tom 179 / 2003

Fundamenta Mathematicae 179 (2003), 27-41 MSC: Primary 26A15; Secondary 26A18, 26A21, 54C30, 37E99. DOI: 10.4064/fm179-1-3

#### Streszczenie

We show that the Sharkovski{ĭ} ordering of periods of a continuous real function is also valid for every function with connected $G_\delta$ graph. In particular, it is valid for every ${\rm DB}_1$ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected $G_\delta$ graph.