Codimension of compact $M$-semilattices
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- by J. W. Lea and A. Y. W. Lau
- Proc. Amer. Math. Soc. 52 (1975), 406-408
- DOI: https://doi.org/10.1090/S0002-9939-1975-0374324-6
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Abstract:
This paper is a generalization of [5] and gives a partial answer to Question 31 in [1], i.e., if $S$ is a compact $M$-semilattice of finite codimension and $x \ne y$, then there exists a closed subsemilattice $A$ of $S$ such that $A$ separates $x$ and $y$ in $S$ and $\operatorname {cd} A < \operatorname {cd} S$.References
- D. R. Brown and A. R. Stralka, Problems on compact semilattices, Semigroup Forum 6 (1973), no. 3, 265–270. MR 372109, DOI 10.1007/BF02389132
- J. D. Lawson, Topological semilattices with small semilattices, J. London Math. Soc. (2) 1 (1969), 719–724. MR 253301, DOI 10.1112/jlms/s2-1.1.719
- J. D. Lawson, Dimensionally stable semilattices, Semigroup Forum 5 (1972/73), 181–185. MR 316326, DOI 10.1007/BF02572890
- J. D. Lawson, The relation of breadth and codimension in topological semilattices. II, Duke Math. J. 38 (1971), 555–559. MR 282891, DOI 10.1215/S0012-7094-71-03868-3
- J. W. Lea Jr., The codimension of the boundary of a lattice ideal, Proc. Amer. Math. Soc. 43 (1974), 36–38. MR 371754, DOI 10.1090/S0002-9939-1974-0371754-2
- E. D. Shirley and A. R. Stralka, Homomorphisms on connected topological lattices, Duke Math. J. 38 (1971), 483–490. MR 279776, DOI 10.1215/S0012-7094-71-03857-9
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 406-408
- MSC: Primary 22A99
- DOI: https://doi.org/10.1090/S0002-9939-1975-0374324-6
- MathSciNet review: 0374324