[0V8] Let \((X,d_ X)\) and \((Y,d_ Y)\) be metric spaces, with \((X,d_ X)\) compact; suppose that \(f:X→ Y \) is continuous and injective. Show that \(f\) is a homeomorphism between \(X\) and its image \(f(X)\).
[0V9]↺↻
(See [0J8]↺↻ for the case of topological space).
