Sequential spaces are a kind of nice topological space.
A sequential topological space is a topological space such that a subset of is closed if (hence iff) it contains all the limit points of all sequences of points of —or equivalently, such that is open if (hence iff) any sequence converging to a point of must eventually be in .
Every Frechet–Uryson space is a sequential space.
Every quotient of a sequential space is sequential. In particular, every CW complex is also a sequential space. (Conversely, every sequential space is a quotient of a metrizable space, giving the alternative definition).
The category of sequential spaces is a coreflective subcategory of the category of all topological spaces.