Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T22:45:51.415Z Has data issue: false hasContentIssue false
  • English
  • Français

Disjoint embeddings of compacta

Part of: Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  26 February 2010

Howard Becker ,
Fons van Engelen  and
Jan van Mill
Howard Becker
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.
Fons van Engelen
Affiliation:
Econometric Institute, Erasmus University Rotterdam, Postbus 1738, 3000 DR Rotterdam, The Netherlands.
Jan van Mill
Affiliation:
Department of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan 1018a, 1081 HV Amsterdam, The Netherlands.
Get access

Abstract

Let X be a separable and metrizable space containing uncountably many pairwise disjoint copies of the compactum K. We discuss the question whether X must contain K × 2ω.

MSC classification

Secondary: 54C25: Embedding
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 221 - 232
Copyright
Copyright © University College London 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Douwen, Eric K. van. Uncountably many pairwise disjoint copies of one metrizable compactum in another. To be published in Houston J. Math.CrossRefGoogle Scholar
2.Jech, T. J.. Set Theory (Academic Press, New York, 1978).Google Scholar
3.Kechris, A. S. and Moschovakis, Y. N.. Notes on the theory of scales. In Kechris, A. S. and Moschovakis, Y. N. (eds.). Cabal Seminar 76-77, Lect. Notes in Math. 689, 1–53.Google Scholar
4.Kuratowski, K.. Topology I (Academic Press, New York, 1966).Google Scholar
5.Luzin, N. and Sierpiński, W.. Sur quelques propriétés des ensembles (A), Bull. Int. Acad. Sci. Cracovie, Série A Sci;. Math., (1918), 35–48.Google Scholar
6.Mansfield, R. and Weitkamp, G.. Recursive aspects of descriptive set theory (Oxford University Press, New York, 1985).Google Scholar
7.Maudlin, R. D. and Schlee, G. A.. Borel measurable selections and applications of the boundedness principle. Real Analysis Exchange, 15 (1989), 90–113.Google Scholar
8.Mill, J. van. Infinite-dimensional topology (North-Holland, Amsterdam, 1989).Google Scholar
9.Moschovakis, Y. N.. Descriptive Set Theory (North-Holland, Amsterdam, 1980).Google Scholar
10.Solovay, R. M.. On the cardinality of -sets of reals. In Bulloff, J. J., Holyoke, T. C. and Hahn, S. W. (eds.), Foundations of Mathematics, Symposium Papers Commemorating the Sixtieth Birthday of Kurt Gödel (Springer-Verlag, Berlin, 1969).Google Scholar
11.Solovay, R. M.. A model of set theory in which every set is Lebesgue measurable. Ann. of Math., 92 (1970), 1–56.Google Scholar
12.Suslin, M.. Sur une définition des ensembles mesurables B sans nombres transfinis. Comptes Rendus Acad. Sciences Paris, (1917), 88–91.Google Scholar