In this program
- Real numbers and sequences
- Topology and continuity
- Differentiation and integration
- Advanced topics
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
- Intermediate value theorems (with proofs)
- Uniform continuity
- Its distinction from pointwise continuity
Study materials
- Study guideComing soon
- Exam StrategyComing soon
- Common MistakesComing soon
- WorksheetsComing soon
- Word problemsComing soon
- Mixed PracticeComing soon
- Multi-Unit ProblemsComing soon
- ReviewComing soon
- Practice testComing soon
- Answer keyComing soon
Interactive practice
Quizzes, typed answers, and flashcards for this unit — coming soon.
- Coming soon
Quiz
Multiple-choice questions with instant feedback
- Coming soon
Typed practice
Type answers and check them
- Coming soon
Flashcards
Vocabulary and key facts
- Coming soon
Mixed quiz
Harder mixed review for this standard