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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Locally convex topological lattices


Author: Albert R. Stralka
Journal: Trans. Amer. Math. Soc. 151 (1970), 629-640
MSC: Primary 54.56; Secondary 06.00
MathSciNet review: 0264625
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Abstract: The main theorem of this paper is: Suppose that L is a topological lattice of finite breadth n. Then L can be embedded in a product of n compact chains if and only if L is locally convex and distributive. With this result it is then shown that the concepts of metrizability and separability are equivalent for locally convex, connected, distributive topological lattices of finite breadth.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0264625-4
PII: S 0002-9947(1970)0264625-4
Keywords: Topological lattice, locally convex, compact, connected, separating point, embed, product of compact chains, distributive
Article copyright: © Copyright 1970 American Mathematical Society