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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Topological continuity
A map is continuous when inverse images of open sets are open.
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Homeomorphisms
A homeomorphism is a bijection continuous in both directions.
Open and closed sets
Closed sets have open complements; a set can be both open and closed.
Topological spaces
A topology specifies open sets closed under arbitrary unions and finite intersections.
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.
Knowledge connections
- Open and closed sets · Related · Map context
- Homeomorphisms · Related · Map context
- Topological spaces · Prerequisite · Map context