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.^[1] Fréchet lattices are important in the theory of topological vector lattices.

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 latticePages displaying short descriptions of redirect targets

References

1. Schaefer & Wolff 1999, pp. 234–242.

Bibliography

• Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
• Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.