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Isomorphisms between inverse semigroups of injective transformations

Published online by Cambridge University Press:  09 April 2009

Bridget Bos Baird
Bridget Bos Baird
Affiliation:
State University of New York at Buffalo, Amherst, New York 14226, U.S.A.
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Abstract

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We introduce a class of inverse semigroups of injective transformations and our main result concerns isomorphisms between two such semigroups. This result is then applied to semigroups of homeomorphisms between closed subsets of a T1 topological space, semigroups of homeomorphisms between compact subsets of k-spaces and semigroups of isomorphisms between subsemilattices of semilattices. In the first two cases it is shown that the two inverse semigroups under consideration are isomorphic if and only if the corresponding topological spaces are homeomorphic. In the latter case, the two inverse semigroups are isomorphic if and only if the semilattices are either isomorphic or are dual isomorphic infinite chains.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 2 , March 1977 , pp. 194 - 201
Copyright
Copyright © Australian Mathematical Society 1977

References

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