Re: Homotopic maps
- From: "ptk" <pkornman@xxxxxxx>
- Date: 22 Nov 2005 05:30:57 -0500
No that's false too. Let U = S^{n-1} x (0, \infty) = R^n - {0} and
f:S^{n-1} - S^{n-1} be an inessential map with image S^{n-1}, where all
the S^{n-1}'s are the boundary of the (round) unit ball. Then the
complementary domain of f(S^{n-1}) is open unit ball B, but B is not a
subset of U.
.
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