Cantor's theorem (disambiguation)

Several theorems are associated the name of Georg Cantor:

Set theory

• Cantor's theorem: no set is bijective with its power set
• 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

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

• Cantor's diagonal argument