Fréchet–Urysohn space

In the field of topology, a Fréchet–Urysohn space is a topological space ${\displaystyle X}$ with the property that for every subset ${\displaystyle S\subseteq X}$ the closure of ${\displaystyle S}$ in ${\displaystyle X}$ is identical to the sequential closure of ${\displaystyle S}$ in ${\displaystyle X.}$ Fréchet–Urysohn spaces are a special type of sequential space.

The property is named after Maurice Fréchet and Pavel Urysohn.