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Let X be a normal space with dim X=n and m\\geq n+1. Then the space C*(X,R^m) of all bounded maps from X into R^m equipped with the uniform convergence topology contains a dense G_{\\delta}-subset consisting of maps g such that \\bar{g(X)}\\cap\\Pi^d is at most (n+d-m)-dimensional for every d-dimensional plane \\Pi^d in R^m, where m-n\\leq d\\leq m.\n  Theorem 2. Let X be a metrizable compactum with dim X\\leq n and m\\geq n+1. 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