= Exponential covering of an annulus by a vertical strip
{title2=$e^z:\{a<\operatorname{Re}z<b\}\twoheadrightarrow\{e^a<|w|<e^b\}$}
The complex <complex exponential function> has nonzero derivative and maps the strip onto the <annulus>, with <fibers> given by translations by $2\pi i$. It is locally conformal, but not injective. No <biholomorphism> from the full strip onto an <annulus> exists because the strip is <simply connected space> and the <annulus> has a loop of nonzero <winding number>. The <complex exponential function> is a <covering map> realizing that topological distinction.
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