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On the order scale of a uniform space

Part of: Special properties Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

D. C. Kent
D. C. Kent
Affiliation:
Department of Mathematics Washington State UniversityPullman, Washington 99164, U.S.A.
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Abstract

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The order topology is compact and T2 in both the scale and retracted scale of any uniform space (S, U). if (S, U) is T2 and totally bounded, the Samuel compactification associated with (S, U) can be obtained by uniformly embedding (S, U) in its order retracted scale (that is, the retracted scale with its order topology). This implies that every compact T2 space is both a closed subspace of a complete, infinitely distributive lattice in its order topology, and also a continuous, closed image of a closed subspace of a complete atomic Boolean algebra in its order topology.

MSC classification

Secondary: 54E15: Uniform structures and generalizations 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 248 - 257
Copyright
Copyright © Australian Mathematical Society 1983

References

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