%%This note needs to expanded significantly to discuss singularites more generally outside of complex analysis%% # Singularities in complex analysis A _singularity_ is a point at which a complex function is not a [holomorphic function](Holomorphic%20functions.md). Singularities are categorized in the following way: ## Isolated singularities An isolate singularity is isolated in the sense that it never neighbors any other singularities. ### [[Pole]] ## Extended singularities ## Removable singularities ## Essential singularities This is a singularity that's neither removable nor a [pole](Pole.md)  #MathematicalFoundations/Analysis/ComplexAnalysis #MathematicalFoundations/Analysis