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Realizing isomorphisms of category algebras

Published online by Cambridge University Press:  17 April 2009

Dorothy Maharam  and
A.H. Stone
Dorothy Maharam
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT;
A.H. Stone
Affiliation:
Department of Mathematics, University of Rochester, Rochester, New York, USA.
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Abstract

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Let C(X) denote the complete boolean algebra of Borel sets modulo first category sets of the space X. Given an isomorphism τ between C(X) and C(Y), where X and Y are complete metric spaces, it is shown that there exists a homeomorphism T, between residual subsets A of X and B of Y, that induces τ. When X = Y one can make A = B. An analogous result is stated when τ is a complete isomorphism onto a subalgebra.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 1 , August 1978 , pp. 5 - 10
Copyright
Copyright © Australian Mathematical Society 1979

References

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