Graph closures and metric compactifications of 𝑁

Steiner, A. K.; Steiner, E. F.

doi:10.1090/S0002-9939-1970-0264614-5

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
DOI: https://doi.org/10.1090/S0002-9939-1970-0264614-5
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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