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Characterizations of compactness of the interval topology in semilattices

Authors: T. B. Muenzenberger and R. E. Smithson
Journal: Proc. Amer. Math. Soc. 46 (1974), 133-136
MSC: Primary 06A20
MathSciNet review: 0345885
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Abstract: In a semilattice two necessary and sufficient conditions for the interval topology to be compact are established. One is in terms of the fixed point property for increasing functions on the semilattice, and the other is in terms of completeness of the semilattice.

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  • [1] A. C. Davis (A. C. Morel), A characterization of complete lattices, Pacific J. Math. 5 (1955), 311-319. MR 17, 574. MR 0074377 (17:574e)
  • [2] T. B. Muenzenberger and R. E. Smithson, Fixed point structures, Trans. Amer. Math. Soc. 184 (1973), 153-173. MR 0328900 (48:7242)
  • [3] R. E. Smithson, Fixed points of order preserving multifunctions, Proc. Amer. Math. Soc. 28 (1971), 304-310. MR 43 #114. MR 0274349 (43:114)
  • [4] -, Fixed points in partially ordered sets, Pacific J. Math. 45 (1973), 363-367. MR 0316323 (47:4871)
  • [5] L. E. Ward, Jr., Completeness in semi-lattices, Canad. J. Math. 9 (1957), 578-582. MR 19, 938. MR 0091264 (19:938a)

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Keywords: Fixed point property, increasing functions, lattices, semilattices
Article copyright: © Copyright 1974 American Mathematical Society

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