Compactness
General · Mathematics
Study notes
Q: Is (0,1) compact? Prove [0,1] is compact via Heine-Borel. (0,1): cover {(1/n,1)}: no finite subcover (0 escapes!): NOT compact! [0,1]: closed + bounded in ℝ: COMPACT (Heine-Borel!)! Every sequence has convergent subsequence! Continuous f: attains max/min (extreme value!)!