Re: Continuous bijection (not necessarily homeo)

On 4 Giu, 13:51, Harun Al-Rashid <ab...@xxxxxxxxxxx> wrote:
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

Hi. You can use this theorem:
If A is a connected set and f a continuous function then f(A) is
connected.
{z in C | |z| < 2} is connected and {z in C | |z| < 2 and z is not in
[-1,1]} not.
.