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absolute retract absolutely continuous affirmative answer analogous answer is negative arbitrary assume Banach belong Borel sets boundary bounded sequence bounded variation Cartesian product class of sets closed set compact congruent constant continuous function continuous functions defined continuous mapping convergent sequences convex set countable curve denote Eidelheit Eilenberg elements equation equivalent Euclidean space exist a function exist a sequence exists a method finite number following property function f function f(x,y Hazur Hilbert space homeomorphic I I I I I isometric isomorphic Lebesgue measure linear measurable functions metric space n-dimensional operation original manuscript orthogonal partial derivatives permutations plane player polynomial Prize Problem Prove question real numbers real variable satisfies the condition Schreier Scottish Book sense sequence of numbers set of real sets of measure sin2 solution space of type sphere Steinhaus subsets surface Szpilrajn theorem is true topological spaces transformations type F Ulam zero