Small inductive dimension of completions of metric spaces

Mrówka, S.

doi:10.1090/S0002-9939-97-04132-4

Small inductive dimension of completions of metric spaces
HTML articles powered by AMS MathViewer

by S. Mrówka PDF

Proc. Amer. Math. Soc. 125 (1997), 1545-1554 Request permission

Abstract:

We construct a 0-dimensional metric space which under a special set-theoretic assumption, denoted in the paper as S($\aleph _{0}$), does not have a 0-dimensional completion. Shortly after the submission of the paper for publication R. Dougherty has shown the consistency of S($\aleph _{0}$). (S($\aleph _{0}$) disagrees with the continuum hypothesis.)

References

R. Dougherty, Narrow coverings of $\omega$-product spaces, Ph.D. Dissertation, U. of C., Berkeley, 1984.
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
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
A. R. Pears, Dimension theory of general spaces, Cambridge University Press, Cambridge, England-New York-Melbourne, 1975. MR 0394604
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
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