New properties of Mrowka’s space $\nu \mu _0$
HTML articles powered by AMS MathViewer
- by John Kulesza PDF
- Proc. Amer. Math. Soc. 133 (2005), 899-904 Request permission
Abstract:
We extend the technique of Mrowka to show that his space $\nu \mu _0$ has the property that dim $\nu \mu _0^n = n$ while ind $\nu \mu _0^n = 0$, assuming his extra set-theoretic hypothesis. We also show that $\nu \mu _0$ is $N-$compact, so assuming the extra axiom, there is an $N-$compact metric space with no $N-$compact completion.References
- Randall Dougherty, Narrow coverings of $\omega$-ary product spaces, Ann. Pure Appl. Logic 88 (1997), no. 1, 47–91. MR 1478522, DOI 10.1016/S0168-0072(97)00013-4
- Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
- John Kulesza, An example in the dimension theory of metrizable spaces, Topology Appl. 35 (1990), no. 2-3, 109–120. MR 1058791, DOI 10.1016/0166-8641(90)90096-K
- John Kulesza, Metrizable spaces where the inductive dimensions disagree, Trans. Amer. Math. Soc. 318 (1990), no. 2, 763–781. MR 954600, DOI 10.1090/S0002-9947-1990-0954600-9
- J.S. Kulesza, Dissertation, SUNY at Binghamton, (1987).
- Stanislaw Mrowka, $N$-compactness, metrizability, and covering dimension, Rings of continuous functions (Cincinnati, Ohio, 1982) Lecture Notes in Pure and Appl. Math., vol. 95, Dekker, New York, 1985, pp. 247–275. MR 789276
- S. Mrówka, Small inductive dimension of completions of metric spaces, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1545–1554. MR 1423324, DOI 10.1090/S0002-9939-97-04132-4
- S. Mrowka, Small Inductive Dimension of Completions of Metric Spaces II, Preprint.
- Prabir Roy, Nonequality of dimensions for metric spaces, Trans. Amer. Math. Soc. 134 (1968), 117–132. MR 227960, DOI 10.1090/S0002-9947-1968-0227960-2
Additional Information
- John Kulesza
- Affiliation: Department of Mathematics, George Mason University, Fairfax, Virginia 22030-4444
- Email: jkulesza@gmu.edu
- Received by editor(s): May 2, 1998
- Received by editor(s) in revised form: September 9, 2000
- Published electronically: October 21, 2004
- Communicated by: Alan Dow
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 899-904
- MSC (2000): Primary 54F45
- DOI: https://doi.org/10.1090/S0002-9939-04-07393-9
- MathSciNet review: 2113942