About: Convenient vector space

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In mathematics, convenient vector spaces are locally convex vector spaces satisfying a very mild completeness condition. Traditional differential calculus is effective in the analysis of finite-dimensional vector spaces and for Banach spaces. Beyond Banach spaces, difficulties begin to arise; in particular, composition of continuous linear mappings stop being jointly continuous at the level of Banach spaces, for any compatible topology on the spaces of continuous linear mappings.

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rdf:type	Thing
rdfs:label	Convenient vector space (en)
rdfs:comment	In mathematics, convenient vector spaces are locally convex vector spaces satisfying a very mild completeness condition. Traditional differential calculus is effective in the analysis of finite-dimensional vector spaces and for Banach spaces. Beyond Banach spaces, difficulties begin to arise; in particular, composition of continuous linear mappings stop being jointly continuous at the level of Banach spaces, for any compatible topology on the spaces of continuous linear mappings. (en)
rdfs:seeAlso	Differentiable vector-valued functions from Euclidean space
foaf:depiction
dcterms:subject	Calculus of variations Differential calculus Multivariable calculus
Wikipage page ID	43466503 (xsd:integer)
Wikipage revision ID	1053096456 (xsd:integer)
Link from a Wikipage to another Wikipage	Bornological space Uniform space Vector space Lie group Compact space Continuous linear operator Tangent bundle Minkowski functional Multivariable calculus Locally convex topological vector space Polar set Banach space Calculus of variations Differential calculus Absolutely convex set Dual space Exponential map (Riemannian geometry) Riemannian manifold A priori estimate Differentiable manifold Cartesian closed category Multivariable calculus Locally convex Nash–Moser theorem Normed vector space Mackey convergent sequence
Link from a Wikipage to an external page	https://arxiv.org/abs/0804.2995 https://arxiv.org/abs/0909.5632 https://arxiv.org/abs/1111.1819 https://arxiv.org/abs/1305.1150 https://arxiv.org/abs/1505.02359 https://www.mat.univie.ac.at/~michor/apbookh-ams.pdf
sameAs	Convenient vector space Convenient vector space Convenient vector space
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has abstract	In mathematics, convenient vector spaces are locally convex vector spaces satisfying a very mild completeness condition. Traditional differential calculus is effective in the analysis of finite-dimensional vector spaces and for Banach spaces. Beyond Banach spaces, difficulties begin to arise; in particular, composition of continuous linear mappings stop being jointly continuous at the level of Banach spaces, for any compatible topology on the spaces of continuous linear mappings. Mappings between convenient vector spaces are smooth or if they map smooth curves to smooth curves. This leads to a Cartesian closed category of smooth mappings between -open subsets of convenient vector spaces (see property 6 below). The corresponding calculus of smooth mappings is called convenient calculus.It is weaker than any other reasonable notion of differentiability, it is easy to apply, but there are smooth mappings which are not continuous (see Note 1).This type of calculus alone is not useful in solving equations. (en)
prov:wasDerivedFrom	wikipedia-en:Convenient_vector_space?oldid=1053096456&ns=0
page length (characters) of wiki page	20784 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Convenient_vector_space
is Link from a Wikipage to another Wikipage of	Calculus of variations Convenient analysis Convenient topological vector space Lie group Diffeomorphism Riemannian manifold Differentiable manifold
is Wikipage redirect of	Convenient analysis Convenient topological vector space
is foaf:primaryTopic of	wikipedia-en:Convenient_vector_space

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