A function space is a collection of functions that share certain properties, allowing them to be treated as a single mathematical entity. These spaces are often defined based on criteria such as continuity, differentiability, or integrability. Common examples include the space of continuous functions, denoted as C(X), where X is a topological space, and the space of square-integrable functions, denoted as L². Function spaces are essential in various fields of mathematics, including functional analysis and differential equations. They provide a framework for studying the behavior of functions and their interactions, enabling mathematicians to apply techniques from linear algebra and topology to analyze complex problems.