Topology
Explore spaces and continuity; global properties and constructions; separation and invariants. Concepts and connections are available independently of video coverage.
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Path connectedness
Every pair of points in a path-connected space can be joined by a continuous path.
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Compactness
A space is compact when every open cover admits a finite subcover.
Connectedness
A connected space cannot be separated into two disjoint nonempty open pieces.
Fundamental group
Based loops modulo endpoint-fixed homotopy form a group under concatenation.
Hausdorff spaces
Distinct points admit disjoint neighborhoods in a Hausdorff space.
Homeomorphisms
A homeomorphism is a bijection continuous in both directions.
Knowledge connections
- Connectedness · Related · Map context
- Compactness · Related · Map context