Nonisolated Singularities
Other than isolated sigularities, complex functions of one variable may exhibit other singular behaviour. Namely, two kinds of nonisolated singularities exist:
- Cluster points, i.e. limit points of isolated singularities: if they are all poles, despite admitting Laurent series expansions on each of them, no such expansion is possible at its limit.
- Natural boundaries, i.e. any non-isolated set (e.g. a curve) which functions can not be analytically continued around (or outside them if they are closed curves in the Riemann sphere).
Read more about this topic: Isolated Singularity