Topologies on products of partially ordered sets. III: Order convergence and order topology. (English) Zbl 0477.06015


06F30 Ordered topological structures
06B30 Topological lattices
06A06 Partial orders, general
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54H12 Topological lattices, etc. (topological aspects)
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
06B10 Lattice ideals, congruence relations
Full Text: DOI


[1] G. Birkhoff,Lattice theory. Amer. Math. Soc. Colloq. Pub. vol.25 (third edition), New York (1967). · Zbl 0153.02501
[2] O. Frink,Topology in lattices, Trans. Amer. Math. Soc.51 (1942), 569–582. · Zbl 0061.39305
[3] A. R. Gingras,Convergence lattices, Rocky Mountain J. Math.6 (1976), 85–104. · Zbl 0333.06006
[4] D. C. Kent,Convergence functions and their related topologies, Fund. Math.54 (1964) 125–133. · Zbl 0122.41301
[5] D. C. Kent,On the order topology in a lattice, Illinois J. Math.10 (1966), 90–96. · Zbl 0131.20401
[6] D. C. Kent,The internal topology and order convergence as dual convergence structures. Amer. Math. Monthly74 (1967) 426–427, 1231–1232. · Zbl 0163.01301
[7] B. C. Rennie Lattices. Proc. London Math. Soc. (2)52 (1951), 386–400. · Zbl 0042.41004
[8] D. P. Strauss,Topological lattices, Proc. London Math. Soc. (3)18 (1968), 217–230. · Zbl 0153.33404
[9] A. J. Ward,On relations between certain intrinsic topologies in partially ordered sets, Proc. Cambridge Phil. Soc.51 (1955), 254–261. · Zbl 0066.02101
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.