Fréchet–Urysohn space

In topology and related fields of mathematics, a sequential space is a topological space that satisfies a very weak axiom of countability. Sequential spaces are the most general class of spaces for which sequences suffice to determine the topology.

Every sequential space has countable tightness.

Let X be a topological space.

The complement of a sequentially open set is a sequentially closed set, and vice versa. Every open subset of X is sequentially open and every closed set is sequentially closed. The converses are not generally true.

A sequential space is a space X satisfying one of the following equivalent conditions:

Given a subset ${\displaystyle A\subset X}$ of a space ${\displaystyle X}$, the sequential closure ${\displaystyle [A]_{\text{seq}}}$ is the set

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