Let be the set of continuous mappings . Then the topological space supplied with the compact-open topology is called a mapping space. If is a pointed space, then the mapping space of pointed maps is called the path space of . In words, is the space of all paths which begin at . is a contractible space with the contraction given by .

# Path Space

## See also

Loop Space, Mapping Space
*This entry contributed by John Renze*

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## References

Bredon, G.*Topology and Geometry*New York: Springer-Verlag, p. 456, 1993.Brylinski, J.-L.

*Loop Spaces, Characteristic Classes and Geometric Quantization.*Boston, MA: Birkhäuser, 1993.Iyanaga, S. and Kawada, Y. (Eds.).

*Encyclopedic Dictionary of Mathematics.*Cambridge, MA: MIT Press, p. 658, 1980.

## Referenced on Wolfram|Alpha

Path Space## Cite this as:

Renze, John. "Path Space." From *MathWorld*--A Wolfram Web Resource, created by Eric W. Weisstein.
https://mathworld.wolfram.com/PathSpace.html