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A
conditionally compact point set with noncompact closure
David Edwin Cook |
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Vol. 35 (1970), No. 2, 313–319
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Abstract |
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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. |
Mathematical Subject Classification
Primary: 54.38
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Milestones
Received: 18 December 1969
Published: 1 November 1970
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Authors |
| David Edwin Cook | |
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