Function Space
f(I) is the collection of all real-valued continuous functions defined on some interval I. f^((n))(I) is the collection of all functions in f(I) with continuous nth derivatives. A function space is a topological vector space whose "points" are functions.
See also
Functional, Functional Analysis, OperatorExplore with Wolfram|Alpha
WolframAlpha
More things to try:
Cite this as:
Weisstein, Eric W. "Function Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FunctionSpace.html