nLab
Frechet-Uryson space

Frechet–Urysohn spaces

Idea

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

Definition

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.

Examples

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

Properties

Every Frechet–Uryson space is a sequential space.

Revised on December 13, 2009 03:43:45 by Toby Bartels (173.60.119.197)