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In complex analysis, a branch of mathematics, an isolated singularity is one that has no other singularities close to it. In other words, a complex number ''z0'' is an isolated singularity of a function ''f'' if there exists an open disk ''D'' centered at ''z0'' such that ''f'' is holomorphic on ''D'' \ , that is, on the set obtained from ''D'' by taking ''z0'' out. Formally, and within the general scope of functional analysis, an isolated singularity for a function is any ''topologically isolated'' point within an open set where the function is defined. Every singularity of a meromorphic function is isolated, but isolation of singularities is not alone sufficient to guarantee a function is meromorphic. Many important tools of complex analysis such as Laurent series and the residue theorem require that all relevant singularities of the function be isolated. There are three types of singularities: removable singularities, poles and essential singularities. ==Examples== *The function has 0 as an isolated singularity. *The cosecant function has every integer as an isolated singularity. 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「isolated singularity」の詳細全文を読む スポンサード リンク
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