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In mathematics, specifically set theory, a continuous function is a sequence of ordinals such that the values assumed at limit stages are the limits (limit suprema and limit infima) 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, ''s'' is continuous if ''s'': γ → range(s) 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. ==References== * Thomas Jech. ''Set Theory'', 3rd millennium ed., 2002, Springer Monographs in Mathematics,Springer, ISBN 3-540-44085-2 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Continuous function (set theory)」の詳細全文を読む スポンサード リンク
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