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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Chains which are coset spaces of $ tl$-groups


Author: Robert L. Madell
Journal: Proc. Amer. Math. Soc. 25 (1970), 755-759
MSC: Primary 06.75
MathSciNet review: 0263716
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Abstract: Let $ G$ be a lattice-ordered group with a topology with which $ G$ is a Hausdorff topological group and topological lattice. Let $ N$ be a closed prime convex $ l$-subgroup of $ G$ and let $ G/N$ denote the topological chain of right cosets of $ N$. It is shown that if $ G$ is locally compact, locally connected, or locally convex then $ G/N$ is either discrete or has precisely the interval topology.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0263716-7
PII: S 0002-9939(1970)0263716-7
Keywords: Lattice-ordered group, topological group, topological lattice, closed prime convex $ l$-subgroup, coset space
Article copyright: © Copyright 1970 American Mathematical Society