 The notion of closed set is defined above in terms of open sets, a concept that makes sense for topological spaces, as well as for other spaces that carry topological structures, such as metric spaces, differentiable manifolds, uniform spaces, and gauge spaces.An alternative characterization of closed sets is available via sequences and nets.A subset "A" of a topological space "X" is closed in "X" if and only if every limit of every net of elements of "A" also belongs to "A".