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Topological vector spaces
Neighborhoods of the origin
Seminorms and norm
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a e G(A analytic class assume bounded C(Rn CjRn claim closure compact subset completely regular space continuous linear form continuous mapping Conversely convex subset CVb(E CVJE decreasing at infinity deduce defined denote dense Dieudonne equilibrated equivalence class f e C(E fact form f fundamental load fundamental weight Hahn-Banach theorem hence implies K-valued function Lemma LEOPOLDO NACHBIN Let the notation linear combinations localizable locally convex space Minkowsky function modules Moreover need the following norm notice numbers open subset p(Xx Proof of Theorem QED DEFINITION QED LEMMA QED Proof QED PROPOSITION QED REMARK rapidly decreasing real-valued functions satisfied self-adjoint seminorm subalgebra sup-lattice topological space topological vector space topologically linearly upper-semicontinuous vanishes Vb(E vector subspace w e G(W Weierstrass theorem Weierstrass-Stone theorem weighted approximation problem x e F