Re: proof that inverse of continuous function is also continuous?

On Mon, 19 Dec 2005, Stephen J. Herschkorn wrote:
> i.love.jeevitha@xxxxxxxxx wrote:
>
> >Does anyone know a non-analysis proof? e-d proofs are okay, without
> >the mention of metric spaces and such.
>
Good composition and communication style requires subject of discussion to
be included in body of message. That is good idea for in your case you
neglected to include that the continuous function is bijection.

> Any continuous bijection from a compact space to a Hausdorff space is a
> homeomorphism.
>
Indeed, and for a counter example suggested of your observation

f:[0,1) -> S^1, x -> (sin 2pi.x, cos 2pi.x)

is continuous bijection without continuous inverse.
.