×

zbMATH — the first resource for mathematics

Convergence and Cauchy structures on lattice ordered groups. (English) Zbl 0441.06015

MSC:
06F15 Ordered groups
06F30 Ordered topological structures
06B23 Complete lattices, completions
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Richard N. Ball, Topological lattice-ordered groups, Pacific J. Math. 83 (1979), no. 1, 1 – 26. · Zbl 0434.06016
[2] Bernhard Banaschewski, Über die Vervollständigung geordneter Gruppen, Math. Nachr. 16 (1957), 51 – 71 (German). · Zbl 0077.03302
[3] S. J. Bernau, Lateral and Dedekind completion of Archimedean lattice groups, J. London Math. Soc. (2) 12 (1975/76), no. 3, 320 – 322. · Zbl 0333.06008
[4] S. J. Bernau, The lateral completion of an arbitrary lattice group, J. Austral. Math. Soc. 19 (1975), 263 – 289. · Zbl 0314.06011
[5] -, Varieties of lattice groups are closed under \( \mathcal{L}\)-completion, Symposia Math. 21 (1977), 349-355.
[6] Roger Bleier and Paul Conrad, \?*-closures of lattice-ordered groups, Trans. Amer. Math. Soc. 209 (1975), 367 – 387. · Zbl 0321.06019
[7] Bourbaki, Elements of mathematics, General Topology. I, Addison-Wesley, Reading, Mass., 1966. · Zbl 0145.19302
[8] Richard D. Byrd and Justin T. Lloyd, Closed subgroups and complete distributivity in lattice-ordered groups, Math. Z. 101 (1967), 123 – 130. · Zbl 0178.02902
[9] P. F. Conrad, Lattice-ordered groups, Lecture notes, Tulane University, 1970. · Zbl 0258.06011
[10] Paul Conrad, The topological completion and the linearly compact hull of an abelian \?-group, Proc. London Math. Soc. (3) 28 (1974), 457 – 482. · Zbl 0298.06024
[11] Paul Conrad and Donald McAlister, The completion of a lattice ordered group, J. Austral. Math. Soc. 9 (1969), 182 – 208. · Zbl 0172.31601
[12] Ralph E. DeMarr, Order convergence and topological convergence, Proc. Amer. Math. Soc. 16 (1965), 588 – 590. · Zbl 0135.22801
[13] C. J. Everett and S. Ulam, On ordered groups, Trans. Amer. Math. Soc. 57 (1945), 208 – 216. · Zbl 0061.03406
[14] Charles Holland, Extensions of ordered groups and sequence completion, Trans. Amer. Math. Soc. 107 (1963), 71 – 82. · Zbl 0117.26903
[15] G. Otis Kenny, The completion of an abelian \?-group, Canad. J. Math. 27 (1975), no. 5, 980 – 985. · Zbl 0321.06021
[16] D. C. Kent, On the order topology in a lattice, Illinois J. Math. 10 (1966), 90 – 96. · Zbl 0131.20401
[17] D. C. Kent and G. D. Richardson, Regular completions of Cauchy spaces, Pacific J. Math. 51 (1974), 483 – 490. · Zbl 0291.54024
[18] Robert L. Madell, Embeddings of topological lattice-ordered groups, Trans. Amer. Math. Soc. 146 (1969), 447 – 455. · Zbl 0192.36203
[19] Fredos Papangelou, Order convergence and topological completion of commutative lattice-groups, Math. Ann. 155 (1964), 81 – 107. · Zbl 0131.02601
[20] Fredos Papangelou, Some considerations on convergence in abelian lattice-groups, Pacific J. Math. 15 (1965), 1347 – 1364. · Zbl 0146.04802
[21] R. H. Redfield, Ordering uniform completions of partially ordered sets, Canad. J. Math. 26 (1974), 644 – 664. · Zbl 0286.06006
[22] Ellen E. Reed, Completions of uniform convergence spaces, Math. Ann. 194 (1971), 83 – 108. · Zbl 0213.49601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.