A general term relating to a space of functions between two given sets X and Y. If the codomain has further structure (e.g. if Y = ℝ), then functions can be pointwise added and multiplied, forming an algebra, and given a partial order. If the domain X is a topological space, then the space C*(X) of bounded, continuous functions real-valued functions on X can be made into a normed vector space with $\Vert f\Vert ={\text{sup}}_{x\in X}|f\left(x\right)|$. For vector spaces V and W, then Hom(V,W), denoting the space of linear maps from V to W, is a vector space itself. See also C⁰, C¹, C^∞, C^ω‎, L^p.