Graph closures and metric compactifications of $N$
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- by A. K. Steiner and E. F. Steiner
- Proc. Amer. Math. Soc. 25 (1970), 593-597
- DOI: https://doi.org/10.1090/S0002-9939-1970-0264614-5
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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.References
- J. M. Aarts and P. van Emde Boas, Continua as remainders in compact extensions, Nieuw Arch. Wisk. (3) 15 (1967), 34–37. MR 214033
- W. W. Comfort and S. Negrepontis, Homeomorphs of three subspaces of $\beta {\bf {\rm }N}\backslash {\bf {\rm }N}$, Math. Z. 107 (1968), 53–58. MR 234422, DOI 10.1007/BF01111048
- Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
- P. R. Halmos, Permutations of sequences and the Schröder-Bernstein theorem, Proc. Amer. Math. Soc. 19 (1968), 509–510. MR 226590, DOI 10.1090/S0002-9939-1968-0226590-1 J. von Neumann, Charakterisierung des Spektrums eines Integraloperators, Hermann, Paris, 1935.
- A. K. Steiner and E. F. Steiner, Compactifications as closures of graphs, Fund. Math. 63 (1968), 221–223. MR 238270, DOI 10.4064/fm-63-2-221-223
- James A. Yorke, Permutations and two sequences with the same cluster set, Proc. Amer. Math. Soc. 20 (1969), 606. MR 235516, DOI 10.1090/S0002-9939-1969-0235516-7
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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