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Path

A path gamma is a continuous mapping gamma:[a,b]|->C^0, where gamma(a) is the initial point, gamma(b) is the final point, and C^0 denotes the space of continuous functions. The notation for a path parametrized by t is commonly denoted sigma(t).

A graph path is a sequence {x_1,x_2,...,x_n} such that (x_1,x_2), (x_2,x_3), ..., (x_(n-1),x_n) are graph edges of the graph and the x_i are distinct.

A path in a topological space X is a continuous map f:[0,1]->X. Often the name path is given to the image of f.

See also

Arc, Contour, Curve, Eulerian Path, Graph, Graph Cycle, Graph Path, Hamiltonian Path, Path Graph, Pathwise-Connected, Walk

Portions of this entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita and Weisstein, Eric W. "Path." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Path.html

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