Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Small inductive dimension of completions
of metric spaces. II


Author: S. Mrówka
Journal: Proc. Amer. Math. Soc. 128 (2000), 1247-1256
MSC (1991): Primary 54F45; Secondary 54A35, 54E35, 54H05
DOI: https://doi.org/10.1090/S0002-9939-99-05162-X
Published electronically: July 8, 1999
MathSciNet review: 1641073
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Extending the results of a previous paper under the same title we show that, under $\mathbf{S}({\aleph _{0}})$, $\operatorname{ind}{}_{c}\, \nu \mu _{0}^{2} = 2$.


References [Enhancements On Off] (What's this?)

  • [Dou] R. Dougherty, Narrow coverings of $\omega $-ary product spaces, Annals of Pure and Applied Logic 88 (1997), 47-91. CMP 98:03
  • [Ku1] John Kulesza, An example in the dimension theory of metrizable spaces, Topology and its appl. 35 (1990), 109 - 120.MR 91g:54045
  • [Ku2] John Kulesza, Metrizable spaces where the inductive dimensions disagree, Trans. A.M.S. 318 , no. 2 . (1990), 763-781. MR 90g:54030
  • [M1] S. Mrówka, Further results on E-compact spaces, Acta Math. 120 (1968), 161 - 185. MR 37:2165
  • [M2] -, Small inductive dimension of completions of metric spaces, Proc. Amer. Math. Soc. 125 (5) (1997), 1545 - 1554. MR 97i:54043
  • [M3] -, $N$-compactness, metrizability and covering dimension, Rings of continuous functions, Marcell Dekker, Inc., New York and Basel, 1985, pp. 248 - 275.MR 86i:54034
  • [Ost] A. Ostaszewski, A note on the Prabir Roy space, Topology Appl. 35, no. 2-3, (1990), 95-107.MR 91j:54060
  • [R] P. Roy, Failure of equivalence of dimension concepts for metric spaces, Bull. A.M.S. 68 (1962), 609 - 613.MR 25:5495

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54F45, 54A35, 54E35, 54H05

Retrieve articles in all journals with MSC (1991): 54F45, 54A35, 54E35, 54H05


Additional Information

S. Mrówka
Affiliation: Department of Mathematics, State University of New York at Buffalo, 134 Defendorf Hall, Buffalo, New York 14224
Email: mrowka@acsu.buffalo.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05162-X
Keywords: Inductive and covering dimension, metric spaces, completion, Bernstein sets, scattered sets
Received by editor(s): March 9, 1998
Received by editor(s) in revised form: June 4, 1998
Published electronically: July 8, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society