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See [[Removable set|Removable set]]. ...removed is called a removable singularity, or a [[Removable singular point|removable singular point]], for this function (class of functions).

...be an [[Analytic function|holomorphic function]]. Then $z_0$ is called a ''removable singular point'' of the function $f$ if there is a positive radius $r_0$ su ...]]; [[Essential singular point|Essential singular point]]; [[Removable set|Removable set]].

...ses; in other words, the question of "elimination" or "removal" of the singularity $K$. See also [[Removable set|Removable set]].

...case the limit belongs to $\mathbb C$, or a [[Pole (of a function)|pole]]. Removable singularities, poles and essential singularities can also be characterized ...he [[Cluster set|cluster set]] of an analytic function $f$ at an essential singularity. A stronger theorem from which the Casorati-Sokhotskii-Weierstrass theorem

..._n=0$ for every $n<0$ then $z_0$ is a [[Removable singular point|removable singularity]]: in this case the limit in \eqref{e:limit} is $a_0$ and $f$ can be extend ...$f$ is defined, such that $z_n \to z_0$ and $f(z_n) \to w$, then poles and removable singularities are characterized by the property that $C (z_0, f)$ consists

complex critical points. The codimension of a singularity (that is, of a germ $ f $ ...its parameter space. The most important result here is Mather's theorem: A singularity $ f $

==Fuchsian singularity of a system== is called ''Fuchsian'' (or Fuchsian singularity), if the matrix of coefficients $A(t)$ is defined in a punctured neighborho

...includes theorems on removable singularities (removability of an isolated singularity of a bounded holomorphic function, removability of a rectifiable singular c ...e domains, theorems on the removability of compact singularity sets and of singularity sets of codimension $ \geq 2 $,

singularity; any subset in $ J ^ {k} ( m, n) $ is called a universal class of singularities (or a universal singularity if $ S $

...phically continued onto the whole domain $ D $ (see also [[Removable set|Removable set]]). The natural domains of existence of holomorphic functions are somet ...be defined so as to remain analytic is called a [[Removable singular point|removable singular point]].