A type of nearest point set in a complete 𝑙-group

Keisler, Michael

doi:10.1090/S0002-9939-1977-0463071-X

A type of nearest point set in a complete $l$-group
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Proc. Amer. Math. Soc. 67 (1977), 189-197 Request permission

Abstract:

A theorem by W. D. L. Appling (Riv. Mat. Univ. Parma, (3) 2 (1973), 251-276) demonstrates that a C-set is a nearest point set in ${\text {ba}}(S,\Sigma )$ with respect to the variation norm. This paper demonstrates an analogous result for a generalized form of C-set in a complete l-group with distance with respect to the norm being replaced by a stronger property definable in a complete l-group (distance between elements x and y of a complete l-group G is taken to be $|x - y|$). The result is then shown to be a characterization of sets possessing the stronger property in the case of a complete vector lattice, but not a characterization in the case of a complete l-group.

References

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