title: Fréchet lattice
text: # Fréchet lattice
  
  In mathematics, specifically in order theory and functional analysis, a Fréchet lattice is a topological vector lattice that is also a Fréchet space. Fréchet lattices are important in the theory of topological vector lattices.
  
  ## Properties
  
  Every Fréchet lattice is a locally convex vector lattice. The set of all weak order units of a separable Fréchet lattice is a dense subset of its positive cone.
  
  ## Examples
  
  Every Banach lattice is a Fréchet lattice.
  
  