Open, closed and compact sets in metric spaces
General · Mathematics
Study notes
Q: Is (0,1) open? Closed? Compact? What about [0,1]? (0,1): OPEN ✓ (balls fit!). Not closed (complement not open: 0 is limit point!). Not COMPACT: cover (1/n, 1): no finite subcover! [0,1]: closed ✓, COMPACT ✓ (Heine-Borel: closed+bounded in ℝ!). (Compact: closed subset of compact!)