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Volume 66—1986

{Page 49}

Distance-Preserving Maps on Abelian Lattice Ordered Groups

Wayne B. Powell
Department of Mathematics, Oklahoma State University, Stillwater OK 74078

It is shown that distance-preserving maps defined on an abelian lattice ordered group determine the cardinal summands, and conversely. Those distance preserving maps defined on sublattices of the abelian lattice ordered group that can be extended to the whole group are characterized. Also, it is shown that an abelian lattice ordered group has the property that all such maps are extendable to the whole group if and only if it is strongly projectable.

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