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- estructura posicional en la que una contracción uniforme de sus puntos siempre tiene un elemento fijo de referencia (es)
- estructura posicional en la que una contracción uniforme de sus puntos siempre tiene un elemento fijo de referencia (es)
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- Let be metric on a vector space such that the topology induced by on makes into a topological vector space. If is a complete metric space then is a complete-TVS. (en)
- Suppose is a complete Hausdorff TVS and is a dense vector subspace of Then every continuous linear map into a complete Hausdorff TVS has a unique continuous linear extension to a map (en)
- Suppose that and are Hausdorff TVSs with complete. Suppose that is a TVS-embedding onto a dense vector subspace of Then
:Universal property: for every continuous linear map into a complete Hausdorff TVS there exists a unique continuous linear map such that
If is a TVS embedding onto a dense vector subspace of a complete Hausdorff TVS having the above universal property, then there exists a unique TVS-isomorphism such that (en)
- Let be a complete TVS and let be a dense vector subspace of
If is any neighborhood base of the origin in then the set
is a neighborhood of the origin in the completion of
If is locally convex and is a family of continuous seminorms on that generate the topology of then the family of all continuous extensions to of all members of is a generating family of seminorms for (en)
- Let be metric on a vector space such that the topology induced by on makes into a topological vector space. If is a complete metric space then is a complete-TVS. (en)
- Let be a metrizable topological vector space and let be a closed vector subspace of Suppose that is a completion of Then the completion of is TVS-isomorphic to If in addition is a normed space, then this TVS-isomorphism is also an isometry. (en)
- The topology of any TVS can be derived from a unique translation-invariant uniformity. If is any neighborhood base of the origin, then the family is a base for this uniformity. (en)
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- Corollary (en)
- Theorem (en)
- Properties of Hausdorff completions (en)
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- Klee (en)
- Completions of quotients (en)
- Topology of a completion (en)
- Existence and uniqueness of the canonical uniformity (en)
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- Complete topological vector space (en)
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