Sometime in 1930, Leo Zippin
showed that there exists a complete Moore space that contains a conditionally
compact point set whose closure is not compact. It is the object of this paper to show
that if the hypothesis of the continuum is true then there exists a separable,
complete Moore space wkick contains such a point set and, furthermore,
satisfies R. L. Moore’s Axioms 2, 3, 4, 5, and 6. Theorem 1, concerning the
existemce of certain subsets of the Cartesian plane, is fundamental to the
construction of this example and its proof constitutes a major portion of this
paper.
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