Abstract
Let X and Y be topological vector spaces, A be a continuous linear map from X to Y, C⊂ X, B be a convex set dense in C, and d∈ Y be a data point. Conditions are derived guaranteeing the set B∩ A −1( d) to be nonempty and dense in C∩ A −1( d). The paper generalizes earlier results by the authors to the case where Y is infinite dimensional. The theory is illustrated with two examples concerning the existence of smooth monotone extensions of functions defined on a domain of the Euclidean space to a larger domain.
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