Cantor's theorem (disambiguation)

Cantor's theorem is a fundamental result in mathematical set theory.

Cantor's theorem may also refer to:

Set theory

• 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

See also

• Georg Cantor
• Cantor's diagonal argument