# Math Help - Homeomorphism

1. ## Homeomorphism

Dear Colleagues,

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

Regards,

Raed.

2. A proof from Munkres "Topology" 2nd edition, page 167 is shown in the image below. Note that a metric space is normal (Th 32.2 in P202 of this textbook) and therefore Hausdorff.