 This implies, by the Bolzano–Weierstrass theorem, that any infinite sequence from the set has a subsequence that converges to a point in the set.Various equivalent notions of compactness, such as sequential compactness and limit point compactness, can be developed in general metric spaces.In contrast, the different notions of compactness are not equivalent in general topological spaces, and the most useful notion of compactness—originally called "bicompactness"—is defined using covers consisting of open sets (see "Open cover definition" below).