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On homoeomorphism of perfect plane sets

Published online by Cambridge University Press:  24 October 2008

A. S. Besicovitch
A. S. Besicovitch
Affiliation:
Trinity College, Cambridge
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Extract

In studying the structure of perfect sets, an important method would be to establish homoeomorphisms in general classes of sets. For then the general structural features of sets could be more easily seen by considering the simplest sets of a homoeomorphic class.

In this paper we establish the homoeomorphism in two general classes of plane perfect sets (we consider only bounded sets).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 2 , April 1958 , pp. 168 - 186
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

REFERENCES

(1)Antoine, L.Sur l'homéomorphie de deux figures et de leurs voisinages, J. Math. Pures Appl. (8) 4 (1921), 221–326.Google Scholar
(2)Trustrum, G. B.J. Lond. Math. Soc. (in the Press).Google Scholar