= Solution
Given a binary cylinder with finite prefix $b_1\ldots b_N$, repeat a finite block beginning with that prefix indefinitely. The resulting binary sequence is periodic under the shift and represents a <periodic point of an interval map> of $F$ in the cylinder. If the given prefix consists entirely of ones, append a zero to the block so that its value is less than one; this still preserves the prefix. Since cylinders can be taken inside any nonempty open interval, \b[periodic points are dense].
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