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An embedding theorem for compact semilattices


Author: J. W. Lea
Journal: Proc. Amer. Math. Soc. 34 (1972), 325-331
MSC: Primary 06A20
DOI: https://doi.org/10.1090/S0002-9939-1972-0437407-5
MathSciNet review: 0437407
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Abstract: It is shown that if a compact topological semilattice S is a topological lattice, then S can be embedded simultaneously algebraically and topologically in a direct product of n chains if and only if S can be algebraically embedded in a direct product of n chains.


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  • [1] K. A. Baker and A. R. Stralka, Compact distributive lattices of finite breadth, Pacific J. Math. 34 (1970), 311-320. MR 0282895 (44:129)
  • [2] G. Birkhoff, Lattice theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R.I., 1967. MR 37 #2638. MR 0227053 (37:2638)
  • [3] R. P. Dilworth, A decomposition theorem for partially ordered sets, Ann. of Math. (2) 51 (1950), 161-166. MR 11, 309. MR 0032578 (11:309f)
  • [4] D. E. Edmondson, A modular topological lattice, Pacific J. Math. 29 (1969), 271-277. MR 39 #4062. MR 0242734 (39:4062)
  • [5] O. Frink, Jr., Topology in lattices, Trans. Amer. Math. Soc. 51 (1942), 569-582. MR 3, 313. MR 0006496 (3:313b)
  • [6] D. P. Strauss, Topological lattices, Proc. London Math. Soc. 18 (1968), 217-230. MR 0227948 (37:3532)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0437407-5
Keywords: Compact semilattice, compact lattice, direct product of chains, meet irreducible
Article copyright: © Copyright 1972 American Mathematical Society

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