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The Borel structure of a hyperspace

Published online by Cambridge University Press:  24 October 2008

D. Hammond Smith
D. Hammond Smith
Affiliation:
University of Exeter
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Extract

In a recent paper (1) Effros defined a topology for the hyperspace of nonempty closed sets of a topological space X, and showed that, if X is polonais, the Borel structure of is standard. We shall show that this conclusion will also follow if X is σ-compact and metrizable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 947 - 948
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Effros, E. G.Convergence of closed subsets in a topological space. Proc. Amer. Math. Soc. 16 (1965), 929–931.CrossRefGoogle Scholar
(2)Kuratowski, C.Topologie. I, 2nd ed., Monografie Mat. 20 (Warsaw, 1948).Google Scholar
(3)Michael, E.Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71 (1951), 152–182.CrossRefGoogle Scholar