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A frame with no admissible topology

Published online by Cambridge University Press:  24 October 2008

John Isbell
John Isbell
Affiliation:
State University of New York at Buffalo
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Extract

Every finitary algebra is, of course, a topological algebra in the discrete topology. On the other hand, a topological Boolean σ-algebra is indiscrete; sequences (0, 0, …, x, x,…) with join x converge to (0, 0,…) with join 0, so 0 is in {x}−, and similarly x is in {0}−. For lattices with infinite joins but only finite meets, such as topologies, the matter is more interesting.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 447 - 448
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

[1] Erné, M. and Gatzke, H.. Meet-continuous lattices in which meet is not continuous. SCS Memo 9/14/82.Google Scholar
[2] Floyd, E. E.. Boolean algebras with pathological order topologies. Pacific J. Math. 5 (1955), 687–689.CrossRefGoogle Scholar
[3] Isbell, J.. Function spaces and adjoints. Math. Scand. 36 (1975), 317–339.CrossRefGoogle Scholar
[4] Johnstone, P. T.. Stone Spaces (Cambridge University Press, 1982).Google Scholar