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Path (topology)
Continuous function whose domain is a closed unit interval / From Wikipedia, the free encyclopedia
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In mathematics, a path in a topological space is a continuous function from a closed interval into
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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 is often denoted
One can also define paths and loops in pointed spaces, which are important in homotopy theory. If is a topological space with basepoint
then a path in
is one whose initial point is
. Likewise, a loop in
is one that is based at
.