Fréchet lattice
{{Short description|Topological vector lattice}}
{{one source|date=June 2020}}
In mathematics, specifically in order theory and functional analysis, a Fréchet lattice is a topological vector lattice that is also a Fréchet space.{{sfn|Schaefer|Wolff|1999|pp=234–242}}
Fréchet lattices are important in the theory of topological vector lattices.
Properties
Every Fréchet lattice is a locally convex vector lattice.{{sfn|Schaefer|Wolff|1999|pp=234–242}}
The set of all weak order units of a separable Fréchet lattice is a dense subset of its positive cone.{{sfn|Schaefer|Wolff|1999|pp=234–242}}
Examples
Every Banach lattice is a Fréchet lattice.
See also
- {{annotated link|Banach lattice}}
- {{annotated link|Locally convex vector lattice}}
- {{annotated link|Join and meet}}
- {{annotated link|Normed lattice}}
- {{annotated link|Vector lattice}}
References
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Bibliography
- {{Narici Beckenstein Topological Vector Spaces|edition=2}}
- {{Schaefer Wolff Topological Vector Spaces|edition=2}}
{{Functional analysis}}
{{Ordered topological vector spaces}}
{{Order theory}}