Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A regular space with a countable network and different dimensions


Authors: George Delistathis and Stephen Watson
Journal: Trans. Amer. Math. Soc. 352 (2000), 4095-4111
MSC (2000): Primary 54F45, 54E20; Secondary 54A25, 54G20
DOI: https://doi.org/10.1090/S0002-9947-00-02473-9
Published electronically: April 19, 2000
MathSciNet review: 1661301
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we construct a regular space with a countable network (even the union of countably many separable metric subspaces) in which $ind$ and $dim$ do not coincide under the assumption of the continuum hypothesis (CH). This gives a consistent negative answer to a question of A.V. Arhangel'skii.


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

  • 1. A. V. Arhangel'skii, A survey of some recent advances in general topology, old and new problems, Actes du congrès international des mathématiciens (Nice, 1970), Tome 2, Gauthier-Villars, 1971, pp. 19-26. MR 55:1269
  • 2. B. Balcar and P. Simon, Disjoint refinement, Handbook of Boolean Algebras, Vol. 2 (J. D. Monk and R. Bonnet, eds.), North-Holland, 1989, pp. 333-386. CMP 21:00
  • 3. R. Engelking, Dimension Theory, North Holland, 1978. MR 58:2753b
  • 4. -, General Topology, Heldermann Verlag, 1989. MR 91c:54001
  • 5. V. V. Fedorcuk, Bicompacta without intermediate dimensions, Soviet Math. Dokl. 14 (1973), 1808-1811.
  • 6. -, Compact spaces without canonically correct sets, Soviet Math. Dokl. 15 (No.5) (1974), 1272-1275.
  • 7. G. Gruenhage, Generalized metric spaces, Handbook of Set-theoretic topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, 1984, pp. 423-501. MR 86h:54038
  • 8. -, Generalized metrics and metrization, Recent progress in general topology (M. Husek and J. van Mill, eds.), North-Holland, 1992, pp. 237-274. CMP 93:15
  • 9. K. Kuratowski, Une application des images de fonctions à la construction de certains ensembles singuliers, Mathematica 6 (1932), 120-123.
  • 10. I. M. Leibo, On the equality of dimensions for closed images of metric spaces, Soviet Math. Dokl. 15 (No. 3) (1974), 835-839.
  • 11. K. Nagami, Dimension for $\sigma$-metric spaces, J. Math. Soc. Japan 23 (1971), 123-129. MR 44:4725
  • 12. S. Oka, Dimension of finite unions of metric spaces, Math. Japon. 24 (1979), 351-362. MR 81d:54028
  • 13. A. R. Pears, Dimension theory of general spaces, Cambridge University Press, 1975. MR 52:15405
  • 14. S. Watson, The construction of topological spaces: Planks and resolutions, Recent progress in general topology (M. Husek and J. van Mill, eds.), North-Holland, 1992, pp. 673-757. CMP 93:15

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 54F45, 54E20, 54A25, 54G20

Retrieve articles in all journals with MSC (2000): 54F45, 54E20, 54A25, 54G20


Additional Information

George Delistathis
Affiliation: Department of Mathematics, York University, 4700 Keele St., North York, Ontario M3J 1P3 Canada

Stephen Watson
Affiliation: Department of Mathematics, York University, 4700 Keele St., North York, Ontario M3J 1P3 Canada
Email: watson@mathstat.yorku.ca

DOI: https://doi.org/10.1090/S0002-9947-00-02473-9
Received by editor(s): February 16, 1996
Received by editor(s) in revised form: November 18, 1998
Published electronically: April 19, 2000
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society