Mapping Space

Let $Y^X$ be the set of continuous mappings $f:X\to Y$. Then the Topological Space for $Y^X$ supplied with a compact-open topology is called a mapping space.

See also Loop Space

References

Iyanaga, S. and Kawada, Y. (Eds.). ``Mapping Spaces.'' §204B in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 658, 1980.