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In mathematics, and especially general topology, the Euclidean topology is an example of a topology given to the set of real numbers, denoted by R. To give the set R a topology means to say which subsets of R 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 R and the empty set ∅ are open sets. == Construction == The set R and the empty set ∅ are required to be open sets, and so we define R and ∅ to be open sets in this topology. Given two real numbers, say ''x'' and ''y'', with we define an uncountably infinite family of open sets denoted by ''S''''x'',''y'' as follows:〔 : Along with the set R and the empty set ∅, the sets ''S''''x'',''y'' with are used as a basis for the Euclidean topology. In other words, the open sets of the Euclidean topology are given by the set R, the empty set ∅ and the unions of various sets ''S''''x'',''y'' for different pairs of (''x'',''y''). 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「Euclidean topology」の詳細全文を読む スポンサード リンク
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