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

See also[]

• Cantor's diagonal argument

Topics referred to by the same term

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