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A complete metrizable locally convex topological vector space.
A Fréchet space is defined by its locally convex topology; no particular compatible complete metric is selected. It need not be normable. Every real or complex Banach space is Fréchet via its norm topology.
wp-frechet-spacenlab-frechet-spaceeom-frechet-spaceEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
For a real or complex locally convex space, require its topology to be Hausdorff, metrizable, and complete for the induced uniformity.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
eom-frechet-spaceEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Schwartz functions form a Fréchet space with seminorms controlling all polynomially weighted derivatives.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-schwartz_spacenlab-schwartz_space