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Categorical characterization of uniform hyperspaces

Published online by Cambridge University Press:  24 October 2008

J. M. Harvey
J. M. Harvey
Affiliation:
Department of Mathematics, University of Zimbabwe, Mount Pleasant, Zimbabwe
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Extract

In this paper, we use categorical methods to arrive at a characterization of Hausdorff hyperspaces of separated uniform spaces within a category of ordered uniform spaces. We begin by showing that the hyperspace construction gives rise to a monad H in the category Uni of non-empty separated uniform spaces and uniformly continuous maps. We then identify the category of H-algebras and characterize hyperspaces in this context.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 229 - 233
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Hitchcock, A. G. Hyperspaces of uniform spaces. Thesis, Keele University, 1971.Google Scholar
(2)Johnstone, P. T.Stone spaces (Cambridge University Press, 1983).Google Scholar
(3)MacLane, S.Categories for the working mathematician (Springer, Berlin 1971).Google Scholar
(4)Manes, E. G. A triple miscellany: Some aspects of the theory of algebras over a triple. Thesis, Wesleyan University, 1967.Google Scholar
(5)Manes, E. G.Algebraic theories (Springer, Berlin, 1976).CrossRefGoogle Scholar
(6)Michael, E.Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71 (1951), 152182.CrossRefGoogle Scholar
(7)Wyler, O.Algebraic theories of continuous lattices. Continuous lattices, Springer Lecture Notes in Math. vol. 871 (1981), pp. 390413.CrossRefGoogle Scholar