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Simultaneous lattice and topological completion of topological posets. (English) Zbl 0319.54024
MSC:
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
06F30 Ordered topological structures (aspects of ordered structures)
54E15 Uniform structures and generalizations
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References:
[1] B. Banaschewski : Über die Vervollständigung geordneter Gruppen . Math. Nachrichten 16 (1957) 51-71 · Zbl 0077.03302 · doi:10.1002/mana.19570160103
[2] G. Birkhoff : Lattice theory . (Amer. Math. Soc., Providence, 3rd ed. 1967). · Zbl 0153.02501
[3] N. Cameron and J.B. Miller : Topology and axioms of interpolation in partially ordered spaces . J. für die reine u. angewandte Math. (to appear). · Zbl 0312.06008 · doi:10.1515/crll.1975.278-279.1 · crelle:GDZPPN002191164 · eudml:151638
[4] L. Fuchs : Partially ordered algebraic systems . (Pergamon, 1963). · Zbl 0137.02001
[5] R.J. Loy and J.B. Miller : Tight Riesz groups . J. Australian Math. Soc. 13 (1972) 224-240. · Zbl 0243.06011 · doi:10.1017/S1446788700011319
[6] H.M. Macneille : Partially ordered sets . Trans Amer. Soc. 42 (1937) 416-460. · JFM 63.0833.04|0017.33904
[7] A.L. Peressini : Ordered topological vector spaces . (Harper and Row, New York, 1967). · Zbl 0169.14801
[8] R.H. Redfield : Ordering uniform completions of partially ordered sets . Canadian J. Math. 26 (1974) 644-664. · Zbl 0286.06006 · doi:10.4153/CJM-1974-062-4
[9] R.H. Redfield : Uniform subcompletions of Dedekind completions . (preprint, Simon Fraser University, Burnaby, B.C.)
[10] N.R. Reilly : Representations of ordered groups with compatible tight Riesz orders . J. Aust. Math. Soc. (to appear). · Zbl 0311.06012
[11] P. Ribenboim : Théorie des groupes ordonnés . (Universidad Nacional del Sur, Bahia Blanca, 1960). · Zbl 0122.03603
[12] B.F. Sherman : Cauchy completion of partially ordered groups . J. Aust. Math. Soc. (to appear). · Zbl 0294.06015 · doi:10.1017/S1446788700019959
[13] A. Weil : Sur les espaces à structure uniforme et sur la topologie générale . Actualités Sci. Ind. 551 (Paris, 1937). · JFM 63.0569.04|0019.18604
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