Kruse, KarstenKarstenKruse2020-11-102020-11-102019Banach Center Publications (119): 233-258 (2019)http://hdl.handle.net/11420/7800We study spaces CVk(Ω,E) of k-times continuously partially differentiable functions on an open set Ω⊂Rd with values in a locally convex Hausdorff space E. The space CVk(Ω,E) is given a weighted topology generated by a family of weights Vk. For the space CVk(Ω,E) and its subspace CVk0(Ω,E) of functions that vanish at infinity in the weighted topology we try to answer the question whether their elements can be approximated by functions with values in a finite dimensional subspace. We derive sufficient conditions for an affirmative answer to this question using the theory of tensor products.en1730-62992019233258Inst.approximation propertytensor productdifferentiableweightvector-valuedMathematikJournal Article10.4064/bc119-141806.02926Institute of Mathematics of the Polish Academy of SciencesOther