A type of nearest point set in a complete š-group
Michael Keisler Ā· Proceedings of the American Mathematical Society Ā· 1977
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 ba ( S , Ī£ ) {\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 ā y | |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.