Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T16:28:01.471Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Bachmann, H. (1967), Transfiniten Zahlen (Springer, Berlin, 2nd edition).Google Scholar
Munn, W. D. (1966), ‘Uniform semilattices and bisimple inverse semigroups’, Quart. J. Math. Oxford (2), 17, 151–159.Google Scholar
Munn, W. D. (1970), ‘Fundamental inverse semigroups’, Quart. J. Math. Oxford (2), 21, 157–170.Google Scholar
Munn, W. D. (1974) (CFIS), ‘Congruence-free inverse semigroups’, Quart. J. Math. Oxford (2), 25, 463–484.CrossRefGoogle Scholar
Sierpinski, W. (1965), Cardinal and ordinal numbers (2nd rev. edition, Panstowe Wyndawnictwo Naukowe, Warsaw).Google Scholar