Complex singularity
= Complex singularity
= Singularity
{synonym}
A point where a specified complex <function> fails to be <holomorphic>, but which is approached by points of its <domain>. An <isolated singularity> has a punctured <neighbourhood> on which the <function> is <holomorphic>; a <non-isolated singularity> has other <singularities> arbitrarily close to it. The classification as a <removable singularity>, a <pole>, or an <essential singularity> applies to <isolated singularities>.