Chain-complete posets and directed sets with applications

Springer Science and Business Media LLC - Tập 6 - Trang 53-68 - 1976
George Markowsky1
1IBM Research Center, Yorktown Heights, USA

Tài liệu tham khảo

S. Abian and A. B. Brown,A theorem on partially ordered sets with applications to fixed point theorems, Canadian J. of Math.13 (1961), 78–83. Alexandroff and Urysohn,Mémoire sur les espaces compacts, Verh. Akad. Wetensch., Amsterdam14 (1929), 1–96. B. Banaschewski,Hüllensysteme und Erweiterung von Quasiordnungen. Z. Math. Logik Grundl. Math.2 (1956), 117–130. G. Brikhoff,Moore-Smith convergence in general topology, Ann of Math.38 (1937), 39–56. G. Birkhoff,Lattice Theory, A.M.S. Colloquium Publ. Vol. 25, 3rd. ed., Providence, 1967. G. Bruns,A lemma on directed sets and chains, Arch. d. Math.18 (1967), 561–563. J. M. Cadiou,Recursive definitions of partial functions and their computations, Thesis, Stanford University, 1972. P. M. Cohn,Universal Algebra, Harper and Row, New York, 1965. P. Crawley and R. P. dilworth,Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs, NJ, 1973. A. C. Davis,A characterization of complete lattices, Pacific J. Math.5 (1955), 311–319. P. Halmos,Naive Set Theory, D. Van Nostrand, Princeton, 1965. P. Hitchcock and D. Park,Induction rules and termination proofs, inAutomata, Languages, and Programming, M. Nivat, Ed., North-Holland, Amsterdam, 1973. T. Iwamura,A lemma on directed sets (in Japanese), Zenkoku Shijo Sugaku Danwakai262 (1944), 107–111. J. L. Kelley,General Topology, D. Van Nostrand, Princeton, 1955. S. Lang,Analysis II, Addison-Wesley, Reading, Mass., 1969. F. Maeda,Kontinuierliche Geometrien, Springer-Verlag, Berlin, 1958. G. Markowsky,Categories of Chain-Complete Posets, IBM Technical Report RC 5100, T. J. Watson Research Center, Yorktown Heights, N.Y. 10598, 1974. J. Mayer-Kalkschmidt and E. F. Steiner,Some theorems in set theory and applications in the ideal theory of partially ordered sets, Duke Math. J.31 (1964) 287–289. J. B. Miller,Fixed and Rising Points of Continuous Monotone Self-maps, Analysis Paper 1, Monash University, 1973. B. Mitchell,Theory of Categories, Academic Press, NY, 1965. J. Schmidt,Über die Rolle der transfiniten Schlussweisen in einer allgemeinen Idealtheorie, Math. Nachr.7 (1952), 165–182. J. Schmidt,Einige grundlegende Begriffe und Sätze aus der Theorie der Hüllenoperatoren, Ber. Math. Tagung, Berlin, (1953) 21–48. L. A. Skornyakov,Complemented Modular Lattices and Regular Rings, Oliver and Boyd, Edinburgh, 1964. A. Tarski,A lattice theoretical fixpoint theorem and its applications, Pacific J. of Math.5 (1955), 285–309.