Exercise 7, § 4

Let $E,F,G$ be topological spaces and let $f: E\rightarrow F$ and $g: F\rightarrow G$ be continuous mappings such that $(E, f)$, $(F, g)$ and $(E, g\circ f)$ are coverings. (a) Give an example where $f$ and $g\circ f$ have a degree, but where $g$ has no degree.

(b) Give an example where $g$ and $g\circ f$ have a degree, but where $f$ has no degree.