Loterre: Mathematics: path

mathematical analysis > complex analysis > path

topology > general topology > path

path

In mathematics, a path in a topological space ${\\displaystyle X}$ is a continuous function from the closed unit interval ${\\displaystyle [0,1]}$ into ${\\displaystyle X.}$ Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space for which there exists a path connecting any two points is said to be path-connected. Any space may be broken up into path-connected components. The set of path-connected components of a space ${\\displaystyle X}$ is often denoted ${\\displaystyle \\pi _{0}(X).}$

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