The normal completions of certain partially ordered vector spaces
Author:
Alan G. Waterman
Journal:
Proc. Amer. Math. Soc. 25 (1970), 141-144
MSC:
Primary 06.80
DOI:
https://doi.org/10.1090/S0002-9939-1970-0255467-X
MathSciNet review:
0255467
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that the normal completions of certain partially ordered vector spaces are the same as certain other normal completions determined by Dilworth.
- Kirby A. Baker, Free vector lattices, Canadian J. Math. 20 (1968), 58–66. MR 224524, DOI https://doi.org/10.4153/CJM-1968-008-x
- L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864
- R. P. Dilworth, The normal completion of the lattice of continuous functions, Trans. Amer. Math. Soc. 68 (1950), 427–438. MR 34822, DOI https://doi.org/10.1090/S0002-9947-1950-0034822-9
- Zbigniew Semadeni, Spaces of continuous functions on compact sets, Advances in Math. 1 (1965), no. fasc. 3, 319–382. MR 185470, DOI https://doi.org/10.1016/0001-8708%2865%2990041-1 Arlan Ramsay, Personal communication (unpublished).
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Additional Information
Keywords:
Normal completion (completion by cuts),
partially ordered vector spaces
Article copyright:
© Copyright 1970
American Mathematical Society