Two easy examples of zero-dimensional spaces

Mysior, A.

doi:10.1090/S0002-9939-1984-0760954-1

Two easy examples of zero-dimensional spaces
HTML articles powered by AMS MathViewer

by A. Mysior PDF

Proc. Amer. Math. Soc. 92 (1984), 615-617 Request permission

Abstract:

We present simple examples of a realcompact zerodimensional space which is not $N$-compact and an $N$-compact space which is not strongly zerodimensional.

References

Samuel Broverman, Another realcompact, $0$-dimensional, non-$N$-compact space, Proc. Amer. Math. Soc. 69 (1978), no. 1, 156–158. MR 467678, DOI 10.1090/S0002-9939-1978-0467678-6
Eric K. van Douwen, A technique for constructing honest locally compact submetrizable examples, Topology Appl. 47 (1992), no. 3, 179–201. MR 1192308, DOI 10.1016/0166-8641(92)90029-Y
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
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
S. Mrówka, Recent results on $E$-compact spaces, TOPO 72—general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), Lecture Notes in Math., Vol. 378, Springer, Berlin, 1974, pp. 298–301. MR 0362231
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
E. Pol, A remark about the Juhász-Kunen-Rudin construction of a hereditarily separable non-Lindelöf space, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), no. 9, 749–751 (English, with Russian summary). MR 423320
E. Pol, Some examples in the dimension theory of Tychonoff spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), no. 10, 893–897 (English, with Russian summary). MR 425928
Elżbieta Pol and Roman Pol, A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an $N$-compact space of positive dimension, Fund. Math. 97 (1977), no. 1, 43–50. MR 464179, DOI 10.4064/fm-97-1-51-52
Teodor C. Przymusiński, On the dimension of product spaces and an example of M. Wage, Proc. Amer. Math. Soc. 76 (1979), no. 2, 315–321. MR 537097, DOI 10.1090/S0002-9939-1979-0537097-3
Michael L. Wage, The dimension of product spaces, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 10, 4671–4672. MR 507930, DOI 10.1073/pnas.75.10.4671