 This notion is defined for more general topological spaces than Euclidean space in various ways.One such generalization is that a topological space is "sequentially" compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space.The Bolzano–Weierstrass theorem states that a subset of Euclidean space is compact in this sequential sense if and only if it is closed and bounded.