Cantor's theorem (disambiguation)
Several theorems are associated with the name of Georg Cantor:
Set theory
- Cantor's theorem: the cardinality of a power set of a set A is strictly greater than the cardinality of A
- Cantor–Bernstein theorem: cardinality of the class of countable order types equals the cardinality of the continuum
- Cantor–Bernstein–Schröder theorem: injections from A to B and from B to A imply a bijection between A and B
Order theory and model theory
- Cantor's isomorphism theorem: every two countable dense unbounded linear orders are isomorphic
Topology
- Cantor's intersection theorem: a decreasing nested sequence of non-empty compact sets has a non-empty intersection
- Heine–Cantor theorem: a continuous function on a compact space is uniformly continuous
- Cantor–Bendixson theorem: a closed set of a Polish space may be written uniquely as a disjoint union of a perfect set and a countable set
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