In this paper we give a solution to a problem of Kulpa about the interior of the image of certain continuous maps f : X → R~n where X is a compact subset of R~n with non-empty interior. Moreover we show that the image of every continuous map f : X ? R~2 where X is a non-empty compact subset of R~2 and diam f~(-1) f(x)) < 3~(1/2)a_X for every x ∈ Fr X, has non-empty interior.
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