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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Connectedness
A connected space cannot be separated into two disjoint nonempty open pieces.
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Hausdorff spaces
Distinct points admit disjoint neighborhoods in a Hausdorff space.
Path connectedness
Every pair of points in a path-connected space can be joined by a continuous path.
Product and quotient topologies
Product and quotient constructions create topologies compatible with coordinate maps or identifications.
Topological spaces
A topology specifies open sets closed under arbitrary unions and finite intersections.
Fundamental group
Based loops modulo endpoint-fixed homotopy form a group under concatenation.
Knowledge connections
- Path connectedness · Related · Map context
- Product and quotient topologies · Related · Map context
- Topological spaces · Related · Map context
- Hausdorff spaces · Related · Map context