On the minimal overlap problem of Erdös
L Moser (1959)
Acta Arithmetica
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Displaying similar documents to “Maintaining the Minimal Distance of a Point Set in Poly-logarithmic Time.”
On the minimal overlap problem of Erdös
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We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...
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Colloquium Mathematicae
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