Fréchet–Urysohn space

Summary

A Fréchet–Urysohn space is a topological space with the following property. Each point of the closure of a set is the limit of a sequence from that set. So closures, and not only closed sets, can be computed with sequences. Every first-countable space is Fréchet–Urysohn, and every Fréchet–Urysohn space is sequential. The converse implications fail in general.