Reciprocal spiral with its endpoint
= Reciprocal spiral with its endpoint
{title2=$\{t^{-1}e^{2\pi it}:t\ge1\}\cup\{0\}$}
The map $F(s)=se^{2\pi i/s}$ for $s>0$, $F(0)=0$, is <continuous> on $[0,1]$, since $|F(s)|=s$. Its image is the displayed spiral together with its endpoint. The image is <compact> and <path-connected>: between images of $s_0,s_1$ the explicit path is $F((1-u)s_0+us_1)$.