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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Frames associated with an abelian $ l$-group

Author: James J. Madden
Journal: Trans. Amer. Math. Soc. 331 (1992), 265-279
MSC: Primary 06F20; Secondary 18B30, 46S99, 54A05, 54H10
MathSciNet review: 1042288
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Abstract: Every archimedean $ l$-group (lattice-ordered group) with weak unit is shown to be isomorphic to a sub-$ l$-group of the $ l$-group of continuous realvalued functions on a Tychonoff locale canonically associated with the $ l$-group. This strengthens the classical Yosida representation theorem in a useful way. The proof uses methods from universal algebra and is constructive.

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Additional Information

Keywords: Yosida representation, archimedean $ l$-group, relatively uniform convergence, frame, locale, $ \sigma $-frame
Article copyright: © Copyright 1992 American Mathematical Society

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