Dedekind 0.0.0
A structuralist C++23 Module Library
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dedekind::geometry::IsHilbertSpace Concept Referenceexport
module dedekind.geometry

An Inner Product Space where every Cauchy sequence converges. More...

Concept definition

template<typename V, typename F>
concept dedekind::geometry::IsHilbertSpace =
IsInnerProductSpace<V, F> && IsDedekindCompleteField<F>
dedekind::geometry::IsHilbertSpace
An Inner Product Space where every Cauchy sequence converges.
Definition hilbert.cppm:54
dedekind::geometry::IsInnerProductSpace
A field-like vector carrier equipped with an inner product morphism.
Definition inner_product.cppm:71

Detailed Description

An Inner Product Space where every Cauchy sequence converges.

A Hilbert space is the "Seamless" limit of geometric intuition. Completeness of the scalar field is certified via IsDedekindCompleteField<F> (from dedekind.morphologies:archimedean), which requires the scalar to be an Archimedean ordered field. This links the metric-space completeness of H to the order-theoretic completeness (IsDedekindComplete) of its scalar domain.

See also
IsDedekindCompleteField
IsDedekindComplete (dedekind.order)