# Covering space of S^1 and Homomorphisms

Let p: (0,10) --> S^1, p(t) = (cos t, sin t).

Show that p is a local homomorphism, but ((0,10), p) is NOT a covering space of S^1.

https://brainmass.com/math/synthetic-geometry/covering-space-homomorphisms-88733

#### Solution Preview

For x in (0,10) find open U nhood x small

enuf so that f(U) doesn't wrap around ...

#### Solution Summary

Covering space of S^1 and Homomorphisms are investigated and discussed in the solution.

$2.19