Topological Vector Space
A topological vector space is a vector space X over a (topological) field F (typically assumed to be the fields R or C of real or complex numbers, respectively) that is endowed with a topology τ such that both vector addition X×X->X and scalar multiplication F×X->X is τ-continuous. Every topological vector space X is trivially an abelian topological group, and also has a continuous dual space X^* consisting of all continuous linear maps X->F from X to the base field F. Note that while some authors insist that the topology τ be Hausdorff, this restriction is not mathematically necessary. Topological vector spaces are of interest in a number of fields including functional analysis and a number of well-studied classes of spaces (e.g., Banach spaces and Hilbert spaces) are topological vector spaces.
Q_ formal p (D, dλ^2) | F(C^n, dz^n) | A^1(D, dλ^2) | A^2(D, dλ^2) | A^ formal p (D, dλ^2) | A^(- formal a )(D, dλ^2) | A^-∞(D, dλ^2) | BH_( formal p , formal q )^( formal s , formal tau )(R^n, dx^n) | H_2^ formal s (R^n, dx^n) | H_ formal p ^ formal s (R^n, dx^n) | ℬ(D, dλ^2) | L^∞(T;X) | L^ formal p (T;X) | BMO(R^n, dx^n) | BPV([a, b]) | BV(R^n, dx^n) | L_( formal p , formal lambda )^C(R^n, dx^n) | Λ_( formal p , ∞)^ formal s (R^n, dx^n) | Λ_( formal p , formal q )^ formal s (R^n, dx^n) | N_( formal p , formal q , formal r )^ formal s (R^n, dx^n) | ...
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