Fréchet lattice

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In mathematics, specifically in order theory and functional analysis, a Fréchet lattice is a topological vector lattice that is also a Fréchet space 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
• Locally convex vector lattice
• Join and meet
• Normed lattice
• Vector lattice

References[]

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.