Matches in DBpedia 2015-10 for { ?s ?p "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 C∞ if they map smooth curves to smooth curves. This leads to a Cartesian closed category of smooth mappings between c∞-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 }
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- Convenient_vector_space 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 C∞ if they map smooth curves to smooth curves. This leads to a Cartesian closed category of smooth mappings between c∞-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.".