C(X) refers to the set of all continuous functions defined on a topological space X. In mathematical terms, a function is continuous if small changes in the input result in small changes in the output. This concept is fundamental in analysis and topology, as it helps in understanding how functions behave in relation to their domains. The space C(X) can be equipped with various structures, such as a norm or a topology, which allows mathematicians to study properties like convergence and compactness. This makes C(X) an essential object in functional analysis, where it is often used to explore the relationships between different types of functions and their limits.