For fixed $h\in G$, the <conjugation> map is the composite
$$
G\longrightarrow G\times G\times G,
\qquad g\longmapsto(g,h,g^{-1}),
$$
followed by multiplication. Inversion, constant maps, diagonal maps, and multiplication are continuous in a <topological group>, so $c_h(g)=ghg^{-1}$ is continuous.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 151 / 1 / b / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-151/1/b/ii/solution