Functional analysis | Topological vector spaces

Bornology

In mathematics, especially functional analysis, a bornology on a set X is a collection of subsets of X satisfying axioms that generalize the notion of boundedness. One of the key motivations behind bornologies and bornological analysis is the fact that bornological spaces provide a convenient setting for homological algebra in functional analysis. This is becausepg 9 the category of bornological spaces is additive, complete, cocomplete, and has a tensor product adjoint to an internal hom, all necessary components for homological algebra. (Wikipedia).

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Complete category | Topological vector space | John von Neumann | Locally convex topological vector space | Topological space | Countable set | Functional analysis | Vector bornology | Cardinal number | Bornological space | Bornivorous set | Mathematics | Topological ring | Homological algebra | Power set | Absolutely convex set | Category (mathematics) | Isomorphism