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Inverse semigroups of homeomorphisms between open subsets

Published online by Cambridge University Press:  09 April 2009

Bridget Bos Baird
Bridget Bos Baird
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida, U.S.A.
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Abstract

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The symbol IG(X) denotes the inverse semigroup, under composition of functions, of all homeomorphisms between open subsets of a T1 topological space X. The first result is that two such semigroups IG(X) and IG(Y) are isomorphic if and only if the spaces X and Y are homeomorphic. Ideals of IG(X) are next examined and it is shown that for many spaces X the semigroup IG(X) is 0-simple. We also look at congruences on IG(X); one result is that we determine a congruence which in many instances is the largest proper congruence on IG(X).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1977 , pp. 92 - 102
Copyright
Copyright © Australian Mathematical Society 1977

References

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