Topological vector spaces

Bornological space

In mathematics, particularly in functional analysis, a bornological space is a type of space which, in some sense, possesses the minimum amount of structure needed to address questions of boundedness of sets and linear maps, in the same way that a topological space possesses the minimum amount of structure needed to address questions of continuity. Bornological spaces are distinguished by the property that a linear map from a bornological space into any locally convex spaces is continuous if and only if it is a bounded linear operator. Bornological spaces were first studied by George Mackey. The name was coined by Bourbaki after borné, the French word for "bounded". (Wikipedia).

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Related pages

Bounded set (topological vector space) | Topological space | Mackey topology | George Mackey | Metrizable topological vector space | Functional analysis | F-space | Bornivorous set | Convex hull | Separable space | Topologies on spaces of linear maps | Topological vector space | Distinguished space | Absorbing set | Banach space | Barrelled space | Strong dual space | Minkowski functional | Hausdorff space | Absolutely convex set | Seminorm | Reflexive space | Continuous linear operator | Mackey space | Bounded set | Fréchet space | LF-space | Mathematics | Field (mathematics) | Ultrabornological space | Locally convex topological vector space | Balanced set | Nicolas Bourbaki | Sequential space | LB-space | Montel space | Complete topological vector space | Convex set