Algebraic Topology
Explore paths and coverings; homology; cohomology and applications. Concepts and connections are available independently of video coverage.
FOLLOW AN IDEA
Topological spaces
A topology specifies open sets closed under arbitrary unions and finite intersections.
Explore concept graph · Explore connected videos
Different ways to understand it
No reviewed video yet. Explore the concept in a map or suggest a resource. Suggest a video
More concepts to explore
Cohomology
Dual cochain constructions yield invariants and additional operations such as cup products.
Connectedness
A connected space cannot be separated into two disjoint nonempty open pieces.
Covering spaces
A covering locally maps disjoint sheets homeomorphically onto an open neighborhood.
Homeomorphisms
A homeomorphism is a bijection continuous in both directions.
Homotopy
A homotopy continuously deforms one map into another.
Knowledge connections
- Open and closed sets · Related · Map context
- Homeomorphisms · Related · Map context
- Sets · Related · Map context
- Connectedness · Related · Map context
- Topological continuity · Next concept · Map context
- Sets · Prerequisite · Map context
- Homotopy · Related · Map context
- Cohomology · Related · Map context
- Covering spaces · Next concept · Map context
Appears in these maps
Topology
Explore spaces and continuity; global properties and constructions; separation and invariants. Concepts and connections are available independently of video coverage.