As a <smooth manifold>, $G\cong\mathbb R^*\times\mathbb R$. It has two <connected component>[connected components], distinguished by the sign of $a$: each of $a>0$ and $a<0$ is connected, and a continuous path in $G$ cannot cross $a=0$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 302 / 1 / d / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-302/1/d/i/solution