Bounded Sets in (f)-spaces
نویسنده
چکیده
1. In the theory of (F)-spaces,1 the following two questions arise: (A) Let £ be a metrizable locally convex space; is it true that if every bounded set in E is separable, the space E is separable? (B) Let £ be a metrizable locally convex space, E its completion; is it true that every bounded set in E is contained in the closure of a bounded set of El The purpose of this note is to prove that, if we assume the continuum hypothesis, the answer to both questions is negative.
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