A Type of Nearest Point Set in a Complete l-group
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, Σ) 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. © 1977 American Mathematical Society.
Proceedings of the American Mathematical Society
Keisler, M. (1977). A type of nearest point set in a complete l-group. Proceedings of the American Mathematical Society, 67(2):189-197. doi:10.1090/S0002-9939-1977-0463071-X.