The Heine–Cantor Theorem: Proving it for real functions on a bounded interval is messy. But proving it for continuous functions on a compact metric space, is short, neat and easy.

[comment: doesn't that leave the task of proving a finite interval of the real line is compact? mathwonk]

The Heine–Cantor Theorem: Proving it for real functions on a bounded interval is messy. But proving it for continuous functions on a compact metric space, is short, neat and easy.

The Heine–Cantor Theorem: Proving it for real functions on a bounded interval is messy. But proving it for continuous functions on a compact metric space, is short, neat and easy.

The Heine–Cantor Theorem: Proving it for real functions on a bounded interval is messy. But proving it for continuous functions on a compact metric space, is short, neat and easy.

[comment: doesn't that leave the task of proving a finite interval of the real line is compact? mathwonk]