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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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