HUNTERTUTORING

Topology and continuity

Real analysis · Theoretical / proof-based

Topology of R: open and closed sets, compactness, and the Heine–Borel theorem

Objectives

  • Topology of R: open and closed sets, compactness, and the Heine–Borel theorem
  • Limits of functions; sequential characterization of limits
  • Continuity; extreme value and intermediate value theorems (with proofs)
  • Uniform continuity and its distinction from pointwise continuity

Study materials