Characterizations of compactness of the interval topology in semilattices
HTML articles powered by AMS MathViewer
- by T. B. Muenzenberger and R. E. Smithson PDF
- Proc. Amer. Math. Soc. 46 (1974), 133-136 Request permission
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.References
- Anne C. Davis, A characterization of complete lattices, Pacific J. Math. 5 (1955), 311–319. MR 74377
- T. B. Muenzenberger and R. E. Smithson, Fixed point structures, Trans. Amer. Math. Soc. 184 (1973), 153–173 (1974). MR 328900, DOI 10.1090/S0002-9947-1973-0328900-X
- R. E. Smithson, Fixed points of order preserving multifunctions, Proc. Amer. Math. Soc. 28 (1971), 304–310. MR 274349, DOI 10.1090/S0002-9939-1971-0274349-1
- R. E. Smithson, Fixed points in partially ordered sets, Pacific J. Math. 45 (1973), 363–367. MR 316323
- L. E. Ward Jr., Completeness in semi-lattices, Canadian J. Math. 9 (1957), 578–582. MR 91264, DOI 10.4153/CJM-1957-065-3
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 133-136
- MSC: Primary 06A20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0345885-7
- MathSciNet review: 0345885