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.