An interactive introduction to mathematical analysis. On decreasing nested sequences of non-empty compact setsĬantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections of decreasing nested sequences of non-empty compact sets. If K is a compact metric space then a subset F C(K) of the space of continuous complex-valued functions on K equipped with the uniform distance, is compact if and only if it is closed, bounded and equicontinuous.
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