Frechet-Uryson space

Frechet–Urysohn spaces


A Frechet–Urysohn (or Frechet–Uryson) space is a topological space in which the closure of a subspace may be described using only sequences.


Recall that, given any subset AA of any topological space, a point xx belongs to the closure of AA if and only if xx is a limit point of at least one net whose elements belong to AA.

A topological space is Frechet–Uryson (or Frechet–Urysohn) if a point xx of the closure of any given subset AA of XX is a limit point of at least one sequence whose elements belong to AA.


Every first-countable space is a Frechet–Uryson space.


Every Frechet–Uryson space is a sequential space.

Last revised on December 13, 2009 at 03:43:45. See the history of this page for a list of all contributions to it.