Logarithmic spiral as an embedded real line
= Logarithmic spiral as an embedded real line
{title2=$h(t)=e^t(\cos t,\sin t)$}
The map $h$ is a <homeomorphism> from the <real line> to its image with the <subspace topology>: its continuous inverse is $h^{-1}(x,y)=\log\sqrt{x^2+y^2}$. Different parameters have different radii, so winding does not destroy injectivity. The origin is an accumulation point of the spiral but is not a point of this space.