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In general topology, a branch of mathematics, the Appert topology, named for , is an example of a topology on the set } of positive integers. To give Z+ a topology means to say which subsets of Z+ are open in a manner that satisfies certain axioms: # The union of open sets is an open set. # The finite intersection of open sets is an open set. # Z+ and the empty set ∅ are open sets. In the Appert topology, the open sets are those that do not contain 1, and those that asymptotically contain almost every positive integer. == Construction == Let ''S'' be a subset of Z+, and let denote the number of elements of ''S'' which are less than or equal to ''n'': : In Appert's topology, a set ''S'' is defined to be open if either it does not contain 1 or N(''n'',''S'')/''n'' tends towards 1 as ''n'' tends towards infinity:〔 : The empty set is an open set in this topology because ∅ is a set that does not contain 1, and the whole set Z+ is also open in this topology since : meaning that for all ''n''. 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「Appert topology」の詳細全文を読む スポンサード リンク
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