(追記) (追記ここまで)
Essential Discontinuity
Any discontinuity that is not removable. That is, a place where a graph is not connected and cannot be made connected simply by filling in a single point. Step discontinuities and vertical asymptotes are two types of essential discontinuities.
Formally, an essential discontinuity is a discontinuity at which the limit of the function does not exist.
See also