A space is compact if every open cover has a finite subcover. Heine-Borel: in ℝⁿ, compact ⇔ closed and bounded. Extreme-value theorem: continuous f on a compact K attains its max/min.
A space is compact if every open cover has a finite subcover. Heine-Borel: in ℝⁿ, compact ⇔ closed and bounded. Extreme-value theorem: continuous f on a compact K attains its max/min.