Dear Colleagues,

Let $\displaystyle X$ and $\displaystyle Y$ be metric spaces, $\displaystyle X$ compact, and $\displaystyle T:X\longrightarrow Y$ bijective and continuous. Show that $\displaystyle T$ is a homeomorphism i.e. $\displaystyle T^{-1}$ is continuous.

Could you please help me in solving this problem.

Regards,

Raed.