A general time scale is oven denoted by
Let t be a point in the time scale.
We then make the following definitions.
1. The forward jump operator is the closest point to t on the right.
2. The backward jump operator is the closest point to t on the left.
3. The graininess is the distance from t to its closest point on the right.
These definitions are illustrated in the following figure.
4. The time scale is said to be right scattered at point t if
This is illustrated in the following figure.
5. The time scale is said to be left scattered at point t if
This is illustrated in the following figure.
6. The time scale is said to be right continuous at point t if
7. The time scale is said to be left continuous at point t if
