In mathematics, a path in a topological space X is a continuous function f from the unit interval I = [0,1] to X

f : I → X.

The initial point of the path is f(0) and the terminal point is f(1). One often speaks of a "path from x to y" where x and y are the initial and terminal points of the path. Note that a path is not just a subset of X which "looks like" a curve, it also includes a parameterization. For example, the maps f(x) = x and g(x) = x² represent two different paths from 0 to 1 on the real line.