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Reflexive Topological Semilattices

Published online by Cambridge University Press:  20 November 2018

S. S. Hong  and
L. D. Nel
S. S. Hong
Affiliation:
Sogang University, Seoul, Korea and Carleton University, Ottawa, Canada
L. D. Nel
Affiliation:
Sogang University, Seoul, Korea and Carleton University, Ottawa, Canada
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The duality between compact 0-dimensional semilattices and discrete semilattices studied by K. H. Hofmann et al. [2] is here extended to larger categories of topological semilattices.

We regard topological semilattices as objects in the category CvSl of convergence semilattices, believing CvSl to be the appropriate setting for this study. The referee objected to this at first, which prompted us to set forth more carefully our reasons for doing so, as follows.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 471 - 482
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Binz, E., Continuous convergence on C(X), Springer Lecture Notes in Math. Vol. 469 (1975).Google Scholar
2. Hofmann, K. H., Mislove, M. and Stralka, A., The Pontryagin duality of compact O-dimensional semilattices and its applications, Springer Lecture Notes in Math. Vol. 396 (1974).Google Scholar
3. Kelley, J. L., General Topology, Van Nostrand, Princeton, 1955.Google Scholar
4. Kuratowski, K., Topology, Volumes I and II, Academic Press, New York, 1966 and 1968.Google Scholar
5. Nel, L. D., Convenient topological algebra and reflexive objects, Categorical Topology, Proc. Conf. Berlin 1978, Springer Lecture Notes in Math. Vol. 719 (1979), 259-276.Google Scholar