1. The problem statement, all variables and given/known data How can you prove Heine-Porel (unit interval is compact) theorem by Bolzano-Weierstrass theorem (there is a limit in a continuous and bounded interval)? 3. The attempt at a solution Compact means that the sequence is complete and totally bounded. Unit interval perhaps means a bounded interval of an unit length. I do not see how the continuity in Bolzano-Weierstrass theorem is related to Heine-Porel theorem.