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A compact semilattice on the Hilbert cube with no interval homomorphism


Author: Gerhard Gierz
Journal: Proc. Amer. Math. Soc. 101 (1987), 592-594
MSC: Primary 06B30; Secondary 22A26, 54H12
DOI: https://doi.org/10.1090/S0002-9939-1987-0911014-0
MathSciNet review: 911014
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Abstract | References | Similar Articles | Additional Information

Abstract: An example for a compact semilattice with no interval homomorphism is given. The underlying space of the semilattice is homeomorphic to the Hilbert cube.


References [Enhancements On Off] (What's this?)

  • [1] G. Gierz, et al., A compendium of continuous lattices, Springer-Verlag, Berlin and New York, 1980. MR 614752 (82h:06005)
  • [2] O. H. Keller, Die Homoimorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1981), 748-758. MR 1512740
  • [3] J. D. Lawson, Topological semilattices with small semilattices, J. London Math. Soc. 1 (1969), 719-724. MR 0253301 (40:6516)
  • [4] -, Lattices with no interval homomorphisms, Pacific J. Math. 32 (1970), 459-465. MR 0256363 (41:1019)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0911014-0
Keywords: Compact semilattices, interval homomorphisms
Article copyright: © Copyright 1987 American Mathematical Society

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