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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On semicontinuous linear lattices


Author: Hidegoro Nakano
Journal: Proc. Amer. Math. Soc. 34 (1972), 115-117
MSC: Primary 46A40
DOI: https://doi.org/10.1090/S0002-9939-1972-0293370-1
MathSciNet review: 0293370
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Abstract: Applying spectral theory, we proved that a linear lattice is continuous if and only if it is semicontinuous and uniformly complete. In this paper we give another proof without use of spectral theory.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293370-1
Keywords: Functional analysis, vector lattices
Article copyright: © Copyright 1972 American Mathematical Society