In this program
- Topological spaces
- Separation and countability
- Compactness and connectedness
Compactness and connectedness
Introductory topology · Theoretical / proof-based
Compactness
Objectives
- Compactness
- Sequential compactness in metric spaces
- Heine–Borel
- Bolzano–Weierstrass in R^n
- Connected
- Path-connected spaces
- Compactness of continuous images
- Extreme value theorem (topological proof)
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