Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

New properties of Mrowka's space $\nu\mu_0$

Author(s): John Kulesza
Journal: Proc. Amer. Math. Soc. 133 (2005), 899-904.
MSC (2000): Primary 54F45
Posted: October 21, 2004
MathSciNet review: 2113942
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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 compact, so assuming the extra axiom, there is an compact metric space with no compact completion.

References:

[D]: R. Dougherty, Narrow coverings of $\omega$ -ary product spaces, Annals of Pure and Applied Logic, 88 (1997), 47-91. MR 1478522 (99j:03035)
[E]: R. Engelking, General Topology, Berlin, (1989). MR 1039321 (91c:54001)
[K1]: J.S. Kulesza, An example in the Dimension Theory of Metrizable spaces, Top. Appl., 35 (1990), 109-120. MR 1058791 (91g:54045)
[K2]: J.S. Kulesza, Metrizable Spaces Where the Inductive Dimensions Disagree, Trans. AMS, 318 (1990), 763-781. MR 0954600 (90g:54030)
[K3]: J.S. Kulesza, Dissertation, SUNY at Binghamton, (1987).
[M1]: S. Mrowka, compactness, Metrizability, and Covering Dimension, Rings of Continuous Functions, Marcel Dekker Inc., (1995), 247-275. MR 0789276 (86i:54034)
[M2]: S. Mrowka, Small Inductive Dimension of Completions of Metric Spaces, Proceedings AMS, 125 (1997), 1545-1554. MR 1423324 (97i:54043)
[M3]: S. Mrowka, Small Inductive Dimension of Completions of Metric Spaces II, Preprint.
[R]: P. Roy, Nonequality of Dimensions for Metric Spaces, Transactions AMS, 134 (1968), 117-132. MR 0227960 (37:3544)

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