Continuous function (set theory)
In set theory, a continuous function is a sequence of ordinals such that the values assumed at limit stages are the limits of all values at previous stages. More formally, let γ be an ordinal, and be a γ-sequence of ordinals. Then s is continuous if at every limit ordinal β < γ,
and
Alternatively, if s is an increasing function then s is continuous if s: γ → range is a continuous function when the sets are each equipped with the order topology. These continuous functions are often used in cofinalities and cardinal numbers.
A normal function is a function that is both continuous and increasing.
