Path Space

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 .

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.