Definition:Arc


 * Graph theory:
 * An arc of a directed graph is a line, with a directional arrow, that joins one vertex to another.


 * Geometry:
 * An arc is a specific part of a general curve. Particular usages:
 * Arc of Circle: any part of its circumference;
 * Arc of Cycloid: one of the parts of a cycloid between two cusps.


 * Topology:
 * An arc from $a$ to $b$ in a topological space is a continuous injection $f: I \to T$ such that $\map f 0 = a$ and $\map f 1 = b$.