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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Graph closures and metric compactifications of $ N$

Authors: A. K. Steiner and E. F. Steiner
Journal: Proc. Amer. Math. Soc. 25 (1970), 593-597
MSC: Primary 54.53
MathSciNet review: 0264614
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Abstract: It is shown that all compactifications of the positive integers $ N$ which have metrizable remainders are themselves metrizable. This is done by first proving that each Hausdorff compactification of a noncompact locally compact space is the graph closure in an appropriate space. It is then shown that any two compactifications of $ N$ which have homeomorphic metrizable remainders are homeomorphic.

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Keywords: Compact spaces, compactifications, metric spaces, graph closures
Article copyright: © Copyright 1970 American Mathematical Society