Bornological space
Space where bounded operators are continuous / From Wikipedia, the free encyclopedia
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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.[citation needed] The name was coined by Bourbaki[citation needed] after borné, the French word for "bounded".