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Dense, uniform and densely subuniform chains

Published online by Cambridge University Press:  09 April 2009

C. J. Ash
C. J. Ash
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut, 06268 U.S.A.
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Abstract

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A chain, or linearly ordered set, is densely subuniform if it is dense and for every order type the elements whose corresponding initial sections have this order type, if any, are dense in the chain. It is uniform if all intial sections are isomorphic. This paper gives constructions for densely subuniform chains which are not uniform. The question arises from the study of congruence-free inverse semigroups, but may also have independent interest.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1977 , pp. 1 - 8
Copyright
Copyright © Australian Mathematical Society 1977

References

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