Novak, Dan Generalization of continuous posets. (English) Zbl 0504.06003 Trans. Am. Math. Soc. 272, 645-667 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 14 Documents MSC: 06A06 Partial orders, general 06A15 Galois correspondences, closure operators (in relation to ordered sets) 06B23 Complete lattices, completions Keywords:continuous extension; closure operator; system of subsets; directed subsets; M-complete poset; well below relation; Galois connections; lattice of subsets; lattice of lower ends; M-continuous posets PDFBibTeX XMLCite \textit{D. Novak}, Trans. Am. Math. Soc. 272, 645--667 (1982; Zbl 0504.06003) Full Text: DOI References: [1] Hans-J. Bandelt and Marcel Erné, Representations and embeddings of \?-distributive lattices, Houston J. Math. 10 (1984), no. 3, 315 – 324. · Zbl 0551.06014 [2] Garrett Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications, vol. 25, revised edition, American Mathematical Society, New York, N. Y., 1948. · Zbl 0033.10103 [3] -, Lattice theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1967. [4] Günter Bruns, Distributivität und subdirekte Zerlegbarkeit vollständiger Verbände, Arch. Math. (Basel) 12 (1961), 61 – 66 (German). · Zbl 0118.02502 · doi:10.1007/BF01650523 [5] Alan Day, Filter monads, continuous lattices and closure systems, Canad. J. Math. 27 (1975), 50 – 59. · Zbl 0436.18003 · doi:10.4153/CJM-1975-008-8 [6] M. Erné, Homomorphisms of \( m\)-generated and \( m\)-distributive posets (to appear). [7] Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Jimmie D. Lawson, Michael W. Mislove, and Dana S. Scott, A compendium of continuous lattices, Springer-Verlag, Berlin-New York, 1980. · Zbl 0452.06001 [8] K. H. Hofmann and A. R. Stralka, The algebraic theory of compact Lawson semilattices, Dissertationes Math. 137 (1976), 1-58. [9] Siegfried L. Jansen, Subdirect representation of partially ordered sets, J. London Math. Soc. (2) 17 (1978), no. 2, 195 – 202. · Zbl 0389.06001 · doi:10.1112/jlms/s2-17.2.195 [10] Jimmie D. Lawson, The duality of continuous posets, Houston J. Math. 5 (1979), no. 3, 357 – 386. · Zbl 0428.06003 [11] George Markowsky, Chain-complete posets and directed sets with applications, Algebra Universalis 6 (1976), no. 1, 53 – 68. · Zbl 0332.06001 · doi:10.1007/BF02485815 [12] Jorge Martinez, Unique factorization in partially ordered sets, Proc. Amer. Math. Soc. 33 (1972), 213 – 220. · Zbl 0241.06007 [13] George N. Raney, Completely distributive complete lattices, Proc. Amer. Math. Soc. 3 (1952), 677 – 680. · Zbl 0049.30304 [14] George N. Raney, A subdirect-union representation for completely distributive complete lattices, Proc. Amer. Math. Soc. 4 (1953), 518 – 522. · Zbl 0053.35201 [15] George N. Raney, Tight Galois connections and complete distributivity, Trans. Amer. Math. Soc. 97 (1960), 418 – 426. · Zbl 0098.02703 [16] Jürgen Schmidt, Universal and internal properties of some extensions of partially ordered sets, J. Reine Angew. Math. 253 (1972), 28 – 42. · Zbl 0237.06001 · doi:10.1515/crll.1972.253.28 [17] Jürgen Schmidt, Universal and internal properties of some completions of \?-join-semilattices and \?-join-distributive partially ordered sets, J. Reine Angew. Math. 255 (1972), 8 – 22. · Zbl 0263.06004 · doi:10.1515/crll.1972.255.8 [18] Dana Scott, Continuous lattices, Toposes, algebraic geometry and logic (Conf., Dalhousie Univ., Halifax, N. S., 1971) Springer, Berlin, 1972, pp. 97 – 136. Lecture Notes in Math., Vol. 274. [19] J. B. Wright, E. G. Wagner, and J. W. Thatcher, A uniform approach to inductive posets and inductive closure, Mathematical foundations of computer science (Proc. Sixth Sympos., Tatranská Lomnica, 1977) Springer, Berlin, 1977, pp. 192 – 212. Lecture Notes in Comput. Sci., Vol. 53. · Zbl 0372.06002 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.