List of continuity-related mathematical topics

For other uses, see Continuity.

In mathematics, the terms continuity, continuous, and continuum are used in a variety of related ways.

Continuity of functions and measures

Continuous function
Absolutely continuous function
Absolute continuity of a measure with respect to another measure
Continuous probability distribution: Sometimes this term is used to mean a probability distribution whose cumulative distribution function (c.d.f.) is (simply) continuous. Sometimes it has a less inclusive meaning: a distribution whose c.d.f. is absolutely continuous with respect to Lebesgue measure. This less inclusive sense is equivalent to the condition that every set whose Lebesgue measure is 0 has probability 0.
Geometric continuity
Parametric continuity
Smoothness
Laplace transform - the asymptotic rolloff of the Laplace transform of a function is faster the higher order of continuity the function has.

Continuum (set theory), the real line or the corresponding cardinal number
Linear continuum, any ordered set that shares certain properties of the real line
Continuum (topology), a nonempty compact connected metric space (sometimes a Hausdorff space)
Continuum hypothesis, a conjecture of Georg Cantor that there is no cardinal number between that of countably infinite sets and the cardinality of the set of all real numbers. The latter cardinality is equal to the cardinality of the set of all subsets of a countably infinite set.
Cardinality of the continuum, a cardinal number that represents the size of the set of real numbers