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