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Generalized intervals and topology. (English) Zbl 0362.06018


MSC:

06F30 Ordered topological structures
06F15 Ordered groups
06A06 Partial orders, general
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

References:

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[11] M. Guillaume: Sur les topologies définies à partir d’une relation d’ordre. Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8^\circ 29 (1956), no. 6. · Zbl 0073.27001
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[14] J. L. Kelley: General Topology. D. van Nostrand Co., Inc., Princeton, 1955. · Zbl 0066.16604
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[17] H. Mayer M. Novotný: On some topologies on products of ordered sets. Arch. Math. (Brno) 1 (1965), pp. 251-257. · Zbl 0178.34002
[18] T. Naito: Lattices with \(P\)-ideal topologies. Tohoku Math. J. (2) 12 (1960), pp. 235-262. · Zbl 0094.01801 · doi:10.2748/tmj/1178244439
[19] R. H. Redfield: A topology for a lattice-ordered group. Trans. Amer. Math. Soc. 187 (1974), pp. 103-125. · Zbl 0302.06028 · doi:10.2307/1997045
[20] B. C. Rennie: Lattices. Proc. Lon. Math. Soc. 52 (1951), pp. 386-400. · Zbl 0044.37901
[21] B. C. Rennie: Lattices. Foister & Jagg, Cambridge, 1952. · Zbl 0042.41004
[22] F. Šik: Zur Theorie der halbgeordnete Gruppen. Czech. Math. J. 6 (1956), pp. 1 - 25. · Zbl 0075.01504
[23] A. J. Ward: On relations between certain intrinsic topologies in partially ordered sets. Proc. Cambridge Phil. Soc. 51 (1955), pp. 254-261. · Zbl 0066.02101
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