Algebraic conditions leading to continuous lattices

Lawson, Jimmie D.

doi:10.1090/S0002-9939-1980-0556616-2

Algebraic conditions leading to continuous lattices
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by Jimmie D. Lawson PDF

Proc. Amer. Math. Soc. 78 (1980), 477-481 Request permission

Abstract:

This paper is concerned with sufficient conditions for a meet-continuous lattice L to be a continuous lattice. In §2 this is shown to be true if the prime elements order generate and $(L, \vee )$ is a compact topological semilattice. In §3 it is shown that a meet-continuous lattice with finite breadth is a continuous lattice.

References

Karl H. Hofmann and Jimmie D. Lawson, Irreducibility and generation in continuous lattices, Semigroup Forum 13 (1976/77), no. 4, 307–353. MR 434904, DOI 10.1007/BF02194952
Karl Heinrich Hofmann and Albert Stralka, The algebraic theory of compact Lawson semilattices. Applications of Galois connections to compact semilattices, Dissertationes Math. (Rozprawy Mat.) 137 (1976), 58. MR 427178
Jimmie D. Lawson, Additional notes on continuity in semitopological semigroups, Semigroup Forum 12 (1976), no. 3, 265–280. MR 405381, DOI 10.1007/BF02195932
Jimmie D. Lawson, Intrinsic topologies in topological lattices and semilattices, Pacific J. Math. 44 (1973), 593–602. MR 318031
Jimmie D. Lawson, Intrinsic lattice and semilattice topologies, Proceedings of the University of Houston Lattice Theory Conference (Houston, Tex., 1973) Dept. Math., Univ. Houston, Houston, Tex., 1973, pp. 206–260. MR 0401576
J. D. Lawson, Lattices with no interval homomorphisms, Pacific J. Math. 32 (1970), 459–465. MR 256363
Jimmie D. Lawson, Compact semilattices which must have a basis of subsemilattices, J. London Math. Soc. (2) 16 (1977), no. 2, 367–371. MR 460525, DOI 10.1112/jlms/s2-16.2.367
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
Leopoldo Nachbin, Topology and order, Van Nostrand Mathematical Studies, No. 4, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. Translated from the Portuguese by Lulu Bechtolsheim. MR 0219042
Dana Scott, Continuous lattices, Toposes, algebraic geometry and logic (Conf., Dalhousie Univ., Halifax, N. S., 1971) Lecture Notes in Math., Vol. 274, Springer, Berlin, 1972, pp. 97–136. MR 0404073