Piecewise Continuous Function

A function is piecewise continuous on a closed interval if there is a finite partition such that is continuous on every open subinterval and has a finite limit from within each adjacent open subinterval at its endpoints. The value of at a partition point need not equal either one-sided limit, so the possible discontinuities are removable discontinuities and jump discontinuities.

The definition extends to other intervals by requiring piecewise continuity on every closed bounded subinterval.