Definition:Continuous Mapping

Definition
The concept of continuity makes precise the intuitive notion that a function has no "jumps" at a given point.

Loosely speaking, in the case of a real function, continuity at a point is defined as the property that the graph of the function does not have a "break" at the point.

This concept appears throughout mathematics and correspondingly has many variations and generalizations.

Topology
The most general definition of continuity is the concept as defined in a topological space.