C[0,1] is the set of all continuous functions defined on the closed interval from 0 to 1. This means that any function in C[0,1] does not have any breaks, jumps, or holes in its graph within this range. The functions can take any real values and must be defined for every point between 0 and 1, inclusive. In mathematical terms, C[0,1] is often studied in the context of functional analysis and topology. It is a complete metric space when equipped with the supremum norm, which measures the maximum distance between two functions over the interval. This property makes C[0,1] important in various applications, including differential equations and approximation theory.