|
In mathematics, more specifically general topology, the nested interval topology is an example of a topology given to the open interval (0,1), i.e. the set of all real numbers ''x'' such that . The open interval (0,1) is the set of all real numbers ''between'' 0 and 1; but ''not including'' either 0 or 1. To give the set (0,1) a topology means to say which subsets of (0,1) 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 (0,1) and the empty set ∅ are open sets. == Construction == The set (0,1) and the empty set ∅ are required to be open sets, and so we define (0,1) and ∅ to be open sets in this topology. The other open sets in this topology are all of the form where ''n'' is a positive whole number greater than or equal to two i.e. .〔 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「Nested interval topology」の詳細全文を読む スポンサード リンク
|