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Abstract
Solution by Charles Diminnie and Roger Zarnowski, Angelo State University, San Angelo, IX. The answer is YES. We construct a function f from [0, 1] to [0, 1] that is 0 almost everywhere, yet attains every value in [0, 1] on every subinterval of [0, 1]. Let A be the set of all x E [0, 1] whose ternary expansion has only finitely many Is. We use the convention for numbers with two different ternary expansions that the expansion is not eventually all Os. Thus A is the union of sets
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