Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-07T13:43:06.329Z Has data issue: false hasContentIssue false

Universal Spaces for Closed Images of σ-Discrete Metric Spaces

Published online by Cambridge University Press:  20 November 2018

Kôichi Tsuda*
Affiliation:
Department of Mathematics, Ehime University Matsuyama 790 Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present a proof of a theorem announced by van Douwen concerning existences of universal spaces for certain closed images of σ-discrete metric spaces.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. van Douwen, E. K., A letter of 21 Oct. 1985, from Denton, Texas.Google Scholar
2. van Douwen, E. K., Closed images of a-discrete metrizable spaces, unpublished manuscript [vDu 98] in the list of [7].Google Scholar
3. Engelking, R., Dimension Theory, North-Holland, Amsterdam, 1978.Google Scholar
4. Engelking, R., General Topology, Heldermann Verlag, Berlin, 1989.Google Scholar
5. Hyman, D. M., A note on closed maps and metrizability, Proc. Amer. Math. Soc. 21(1969), 109112.Google Scholar
6. Medvedev, S. V., Zero-dimensional homogeneous Borel sets, Soviet Math. Dokl. 32(1985), 144—147.Google Scholar
7. van Mill, J., In memoriam: Eric Karel van Douwen (1946-1987), Topology Appl. 31(1989), 118.Google Scholar
8. Nagami, K., The equality of dimensions, Fund. Math. 106(1980), 239246.Google Scholar
9. Terada, T., Spaces whose all nonempty clopen subspaces are homeomorphic, Yokohama Math. J., to appear.Google Scholar
10. Tsuda, K., Non-existence of universal spaces for some stratifiable spaces, Topology Proc. 9(1984), 165171.Google Scholar
11. Tsuda, K., Dimension Theory of general spaces, Doctoral dissertation, Univiversity of Tsukuba, 1985.Google Scholar
12. Tsuda, K., A universal space for strongly 0-dimensional closed images of complete metrizable spaces, unpublished manuscript.Google Scholar
13. Tsuda, K., A Black Box Left by Late van Douwen Inside Out, Questions Answers Gen. Topology 11(1993), 1518.Google Scholar
14. Tsuda, K., Universal spaces for 0-dimensional van Douwen-complete spaces, preprint.Google Scholar
15. Tsuda, K., Universal spaces for closed images of a-discrete metric spaces II, in preparation.Google Scholar
16. Tsuda, K. and Watson, S., A universal space for closed images of rationals, Topology Appl. 54( 1993), 6576.Google Scholar