We denote:

- 1.
- The vector function
is continuous at
*t*_{0}if, and only if, each component*F*_{i}is continuous at*t*_{0}. - 2.
- The vector function
is continuous on the open interval
*I*if it is continuous at every point of*I*.

- 1.
- The function is continuous on .
- 2.
- The function
is discontinuous at every point
(with integer
*k*), and continuous at every other point.