Let F be a partially ordered (real) linear space with the positive wedge C. It is known that V has the least upper bound property if and only if V has the Hahn-Banach extension property and C is lineally closed. In recent papers, W. E. Bonnice and R. J. Silverman proved that the Hahn-Banach extension and the least upper bound properties are equivalent. We found that their proof is valid only for a restricted class of partially ordered linear spaces. In the present paper, we supply a proof for

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... e general case. We prove that if V contains a partially ordered linear subspace W of dimension ä 2, whose induced wedge K = WD C satisfies KU ( -K) = W and Kr\(-K) = {zero vector}, then V fails to have the Hahn-Banach extension property. From this the desired result A wedge C is said to be sharp if uEC and -uEC imply that Received by the editors November 18, 1969. A MS 1969 subject classifications. Primary 4620,4650; Secondary 0620.