Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T15:10:21.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuous Images of Compact Semilattices

Published online by Cambridge University Press:  20 November 2018

Murray Bell  and
Jan Pelant
Murray Bell
Affiliation:
Department of Mathematics University of Manitoba Winnipeg, Canada R3T 2N2
Jan Pelant
Affiliation:
Mathematical Institute Czechoslovak Academy of Sciences Praha, Czechoslovakia
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.

Hyadic spaces are the continuous images of a hyperspace of a compact space. We prove that every non-isolated point in a hyadic space is the endpoint of some infinite cardinal subspace. We isolate a more general order-theoretic property of hyerspaces of compact spaces which is also enjoyed by compact semilattices from which the theorem follows.

Keywords

Primary 54B20Secondary 54C05HyadicCompact SemilatticesCardinal Subspaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 109 - 113
Copyright
Copyright © Canadian Mathematical Society 01

References

1. Aumann, G., Uber Räume mit Mittelbildungen, Math. Ann. 119, 1943, 210–215.Google Scholar
2. van Douwen, E., Mappings from hyperspaces and convergent sequences, manuscript.Google Scholar
3. Gierz, G., Hofmann, K., Kiemal, K., Lawson, J., Mislove, M. and Scott, D., A Compendium of Continuous Lattices, Springer-Verlag, 1980.Google Scholar
4. Hofmann, K., Mislove, M. and Stralka, A., The Pontryagin Duality of Compact O-Dimensional Semi lattices and its Applications, Lecture Notes in Mathematics No. 396, Springer-Verlag 1974.Google Scholar
5. Lawson, J., Lattices with no interval homomorphisms, Pac. J. Math. 32 (1970) 459–465.Google Scholar
6. van Mill, J., Supercompactness and Wallman Spaces, Mathematical Centre Tracts 85, Amsterdam 1977.Google Scholar
7. Ostazewski, A., On countable compact, perfectly normal spaces, J. London Math. Soc. (2) 14, 1976, 506–516.Google Scholar