Topological vector spaces

LB-space

In mathematics, an LB-space, also written (LB)-space, is a topological vector space that is a locally convex inductive limit of a countable inductive system of Banach spaces. This means that is a direct limit of a direct system in the category of locally convex topological vector spaces and each is a Banach space. If each of the bonding maps is an embedding of TVSs then the LB-space is called a strict LB-space. This means that the topology induced on by is identical to the original topology on Some authors (e.g. Schaefer) define the term "LB-space" to mean "strict LB-space," so when reading mathematical literature, its recommended to always check how LB-space is defined. (Wikipedia).

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Related pages

Topological space | Support (mathematics) | Topological vector space | Comparison of topologies | Banach space | Barrelled space | Euclidean topology | Hausdorff space | Direct limit | Final topology | Image (mathematics) | Natural number | Mathematics | Ultrabornological space | Fréchet–Urysohn space | Euclidean space | Bornological space | Bijection | Locally convex topological vector space | Sequential space | Subspace topology | Complete topological vector space | Product topology