Fréchet lattice
Topological vector lattice From Wikipedia, the free encyclopedia
In mathematics, specifically in order theory and functional analysis, a Fréchet lattice is a topological vector lattice that is also a Fréchet space.[1] Fréchet lattices are important in the theory of topological vector lattices.
 | This article relies largely or entirely on a single source. (June 2020) |
Properties
Every Fréchet lattice is a locally convex vector lattice.[1] The set of all weak order units of a separable Fréchet lattice is a dense subset of its positive cone.[1]
Examples
Every Banach lattice is a Fréchet lattice.
See also
- Banach lattice – Banach space with a compatible structure of a lattice
- Locally convex vector lattice
- Join and meet – Concept in order theory
- Normed lattice
- Vector lattice – Partially ordered vector space, ordered as a lattice
References
Bibliography
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