Algebraic Topology
Explore paths and coverings; homology; cohomology and applications. Concepts and connections are available independently of video coverage.
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Fundamental group
Based loops modulo endpoint-fixed homotopy form a group under concatenation.
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Covering spaces
A covering locally maps disjoint sheets homeomorphically onto an open neighborhood.
Hausdorff spaces
Distinct points admit disjoint neighborhoods in a Hausdorff space.
Homotopy
A homotopy continuously deforms one map into another.
Connectedness
A connected space cannot be separated into two disjoint nonempty open pieces.
Homeomorphisms
A homeomorphism is a bijection continuous in both directions.
Knowledge connections
- Homotopy · Related · Map context
- Hausdorff spaces · Related · Map context
- Homotopy · Prerequisite · Map context
- Homotopy · Related · Map context
- Covering spaces · Related · Map context
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Topology
Explore spaces and continuity; global properties and constructions; separation and invariants. Concepts and connections are available independently of video coverage.