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In mathematics, more specifically general topology, the divisor topology is an example of a topology given to the set ''X'' of positive integers that are greater than or equal to two, i.e., }. The divisor topology is the poset topology for the partial order relation of divisibility on the positive integers. To give the set ''X'' a topology means to say which subsets of ''X'' are "open", and to do so in a way that the following axioms are met: # The union of open sets is an open set. # The finite intersection of open sets is an open set. # The set ''X'' and the empty set ∅ are open sets. == Construction == The set ''X'' and the empty set ∅ are required to be open sets, and so we define ''X'' and ∅ to be open sets in this topology. Denote by Z+ the set of positive integers, i.e., the set of positive whole number greater than or equal to one. Read the notation ''x''|''n'' as "''x'' divides ''n''", and consider the sets : Then the set ''Sn'' is the set of divisors of ''n''. For different values of ''n'', the sets ''Sn'' are used as a basis for the divisor topology.〔 The open sets in this topology are the lower sets for the partial order defined by 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「Divisor topology」の詳細全文を読む スポンサード リンク
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