A type of nearest point set in a complete -group

Author:
Michael Keisler

Journal:
Proc. Amer. Math. Soc. **67** (1977), 189-197

MSC:
Primary 06A55

DOI:
https://doi.org/10.1090/S0002-9939-1977-0463071-X

MathSciNet review:
0463071

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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 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 ). 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0463071-X

Keywords:
Complete *l*-group,
complete vector lattice,
complex,
*l*-nearest point set,
normal subgroup,
projection operator

Article copyright:
© Copyright 1977
American Mathematical Society