I am a beginner in Topology. I was going through Munkres book where I came across this example. The mapping $[0,1)\to S^1$ (unit circle) is bijective and continuous, but $f^{-1}$ is not continuous. The function $f(t)=(\cos 2\pi t, \sin 2\pi t)$ and $S^1$ is a subspace of the plane $\mathbb{R}^2$. I don't understand how the inverse is not continuous. Can someone please explain this simple thing to me?
Thanks a lot