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The equivalence of the least upper bound property and the Hahn-Banach extension property in ordered linear spaces. (English) Zbl 0221.46007

MSC:
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46A03 General theory of locally convex spaces
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[1] W. E. Bonnice and R. J. Silverman, The Hahn-Banach extension and the least upper bound properties are equivalent, Proc. Amer. Math. Soc. 18 (1967), 843 – 849. · Zbl 0165.46802
[2] William E. Bonnice and Robert J. Silverman, The Hahn-Banach theorem for finite dimensional spaces, Trans. Amer. Math. Soc. 121 (1966), 210 – 222. · Zbl 0133.37104
[3] Ting On To, A note of correction to a theorem of W. E. Bonnice and R. J. Silverman., Trans. Amer. Math. Soc. 139 (1969), 163 – 166. · Zbl 0175.12902
[4] Mahlon M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. Heft 21. Reihe: Reelle Funktionen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. · Zbl 0082.10603
[5] R. J. Silverman and Ti Yen, The Hahn-Banach theorem and the least upper bound property, Trans. Amer. Math. Soc. 90 (1959), 523 – 526. · Zbl 0085.09502
[6] Preston C. Hammer, Maximal convex sets, Duke Math. J. 22 (1955), 103 – 106. · Zbl 0064.16601
[7] V. L. Klee Jr., The structure of semispaces, Math. Scand. 4 (1956), 54 – 64. · Zbl 0070.39203
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