Open neighborhood compact closure everywhere.

In mathematics, a topological space X is sequentially compact if every sequence of points in X has a convergent subsequence converging to a point in .

In the mathematical discipline of functional analysis, the concept of a compact operator on Hilbert space is an extension of the concept of a matrix acting on a finite-dimensional vector space; in Hilbert space, compact operators are precisely the closure of finite-rank operators (representable by finite-dimensional matrices) in the topology induced by the operator norm.