Geodesic
Connectedness Properties of Lattices
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 314-320

Voir la notice de l'article provenant de la source Cambridge University Press

Let L be a lattice and q a convergence structure (or a topology) finer than the interval topology of L. In case of compact maximal chains and continuous lattice translations, the connected components of the space (L,q) are characterized using lattice conditions only. Moreover, lattice conditions of L are related to connectedness conditions of the order convergence space (L, o). Throughout this note, maximal chain conditions and maximal chain techniques play an important role.
DOI : 10.4153/CMB-1986-048-2
Mots-clés : 54A20, 54D05, 54H12, Maximal chains in lattices, convergence structures (topologies) on lattices, order convergence, interval topology, connected components 
Vainio, R. Connectedness Properties of Lattices. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 314-320. doi: 10.4153/CMB-1986-048-2
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[1] 1. Ball, R. N., Convergence and Cauchy structures on lattice ordered groups, Trans. Amer. Math. Soc. 259(1980), pp. 357–392. Google Scholar

[2] 2. Erné, M., On the relativization of chain topologies, Pacific J. Math. 84 (1979), pp. 43 — 52. Google Scholar

[3] 3. Erné, M., Separation axioms for interval topologies, Proc. Amer. Math. Soc. 79 (1980), pp. 185—190. Google Scholar

[4] 4. Erné, M., Scott convergence and Scott topology in partially ordered sets II. in Lecture Notes in Math. 871. Springer-Verlag, Berlin-Heidelberg-New York 1981. Google Scholar

[5] 5. Erné, M., and Week, S., Order convergence in lattices, Rocky Mountain J. Math. 10 (1980), pp. 805–818. Google Scholar

[6] 6. Gähler, W., Grundstrukturen der Analysis I—II, Akademie-Verlag und Birkhäuser Verlag, 1977—78. Google Scholar

[7] 7. Kent, D. C., On the order topology in a lattice, Illinois J. Math. 10 (1966), pp. 90–96. Google Scholar

[8] 8. Rennie, B. C., Lattices, Proc. London Math. Soc. 52 (1951), pp. 386–400. Google Scholar

[9] 9. Vainio, R., The limit space CC(X, Y) and the connected components of X and Y, Math. Nachr. 113 (1983), pp. 29–37. Google Scholar

[10] 10. Vainio, R., On connectedness in limit space theory, Proceedings of the Schwerin 1983 School on Convergence Structures, to appear. Google Scholar

[11] 11. Ward, L. E., Partially ordered topological spaces, Proc. Amer. Math. Soc. 5 (1954), pp. 144—161. Google Scholar

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