Let be the set of continuous mappings . Then the Topological Space for supplied with a compact-open topology is called a Mapping Space, and if is taken as the interval , then is called a loop space (or Space of Closed Paths).

**References**

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.

© 1996-9

1999-05-25