Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T06:57:17.507Z Has data issue: false hasContentIssue false

On the projection of Souslin sets

Published online by Cambridge University Press:  26 February 2010

C. A. Rogers
Affiliation:
University College, London.
R. C. Willmott
Affiliation:
University College, London.
Get access

Extract

In a complete separable metric space the Souslin sets coincide with the analytic sets and the projection properties of the Souslin sets follow from those of the analytic sets. The projection properties of Souslin sets do not seem to have been discussed in more general circumstances when this equivalence to the analytic sets breaks down. The object of this note is to contribute the following result, that applies in these circumstances, and which will be used by Willmott in forthcoming work on the theory of uniformization.

Type
Research Article
Copyright
Copyright © University College London 1966

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. Choquet, G., “Ensembles boréliens et analytiques dans les espaces topologiques”, C.R. Acad. Sci. Paris, 232 (1951), 21742176.Google Scholar
2. Choquet, G., “Theory of capacities”, Ann. Inst. Fourier, Grenoble, 5 (19531954), 131295.CrossRefGoogle Scholar
3. Choquet, G., “Ensembles K-analytiques et K-sousliniens”, Ann. Inst. Fourier, Grenoble, 9 (1959), 7589.CrossRefGoogle Scholar
4. Frolik, Z., “The descriptive theory of sets and spaces”, Proc. Symp. General Topology and its relations to modern analysis and algebra (Prague, 1961), 157173.Google Scholar
5. Rogers, C. A., “Analytic sets in Hausdorff spaces”, Mathematika, 11 (1964), 18.CrossRefGoogle Scholar
6. Rogers, C. A., Descriptive Borel sets”, Proc. Roy. Soc., (A) 286 (1965), 455478.Google Scholar