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A complete normed vector space.
wp-banachnlab-banachprinceton-functional-analysisEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The inner product induces a norm, and Hilbert completeness makes the resulting normed space a Banach space.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-hilbertnlab-hilbertprinceton-functional-analysisThis is an authored directed relation from the source endpoint to the target endpoint.
Require completeness in the norm metric.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-banachnlab-banachprinceton-functional-analysisEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Supply a Banach-space norm over the same normed field and on the same carrier, addition, and scalar action as the algebra.
Feed several structures into a construction junction and impose compatibility between them.
mathlib-normed-algebramathlib-normed-ringThis is an authored directed relation from the source endpoint to the target endpoint.
Sobolev spaces complete functions under norms including weak derivatives.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-sobolev_spacenlab-sobolev_space