##### Wiktionary

**function space**

n. (context mathematics English) Any metric space whose elements are functions

##### Wikipedia

**Function space**

In mathematics, a **function space** is a set of functions of a given kind from a set *X* to a set *Y*. It is called a space because in many applications it is a topological space (including metric spaces), a vector space, or both. Namely, if *Y* is a field, functions have inherent vector structure with two operations of pointwise addition and multiplication to a scalar. Topological and metrical structures of function spaces are more diverse.

#### Usage examples of "function space".

Lorn nods and slips out, past the door to the unused room across the corridor, the room that seems designed to be an audience chamber or some sort of official __function space__.