In this program
- Topology of R: open and closed sets, compactness, and the Heine–Borel theorem
- Limits of functions
- Continuity
- Intermediate value theorems (with proofs)
- Uniform continuity
- Its distinction from pointwise continuity
Topology and continuity
Topology of R: open and closed sets, compactness, and the Heine–Borel theorem
Real analysis · Theoretical / proof-based
Topic
Topology of R: open and closed sets, compactness, and the Heine–Borel theorem
Undergraduate Real Analysis — scope drawn from open analysis notes (e.g. Abbott-style / LibreTexts real analysis sequences) and typical US intro real analysis syllabi.