Re: Continuous bijection (not necessarily homeo)

Hi! My problem is:

Show that there is no continuous bijection from {z in
C | |z| < 2}
to {z in C | |z| < 2 and z is not in [-1,1]}.

(here the real interval [-1,1] is considered as a
subset of C)

TIA

At first glance, if such a map, say f, does exist, then
there is a function delta: (0,2) --> (0, +oo) s.t.
dist( f(z), [-1,1] ) < delta(eps), then |z| > 2 - eps.
Maybe this helps.
.