Another realcompact, $0$-dimensional, non-$N$-compact space
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- by Samuel Broverman
- Proc. Amer. Math. Soc. 69 (1978), 156-158
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467678-6
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Abstract:
A refinement of the topology of the plane is constructed which is locally compact, locally countable, 0-dimensional, realcompact, but not N-compact.References
- S. Broverman, $N$-compactness and weak homogeneity, Proc. Amer. Math. Soc. 62 (1976), no. 1, 173–176 (1977). MR 458369, DOI 10.1090/S0002-9939-1977-0458369-5
- Kim-peu Chew, A characterization of $N$-compact spaces, Proc. Amer. Math. Soc. 26 (1970), 679–682. MR 267534, DOI 10.1090/S0002-9939-1970-0267534-5
- R. Engelking and S. Mrówka, On $E$-compact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 (1958), 429–436. MR 0097042
- 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, DOI 10.1007/978-1-4615-7819-2
- Peter Nyikos, Prabir Roy’s space $\Delta$ is not $N$-compact, General Topology and Appl. 3 (1973), 197–210. MR 324657, DOI 10.1016/0016-660X(72)90012-8
- Prabir Roy, Failure of equivalence of dimension concepts for metric spaces, Bull. Amer. Math. Soc. 68 (1962), 609–613. MR 142102, DOI 10.1090/S0002-9904-1962-10872-6 E. K. van Douwen, A technique for constructing honest locally compact submetrizable examples (preprint).
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 69 (1978), 156-158
- MSC: Primary 54D60
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467678-6
- MathSciNet review: 0467678