Function Space

functional-analysis analysis

Definition

Function Space

Let $X$ and $Y$ be sets. A function space is a collection of functions from $X$ to $Y$ that is regarded as a mathematical object in its own right.

Such a collection may be written as

$$Y^X=\{f:X\to Y\}.$$

In practice, a function space often consists of functions that satisfy additional properties, such as continuity, smoothness, or integrability.