Elementary Algebraic Topology
The Ascoli-Arzelà Theorem is a fundamental result in analysis that provides a characterization of compactness in the space of continuous functions. Specifically, it states that a set of continuous functions is relatively compact in the space of continuous functions if and only if it is uniformly bounded and equicontinuous. This theorem connects the notions of compactness with the behavior of function sequences, making it essential for understanding the properties of function spaces.
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