Vol. 44, No. 1, 1973

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Decomposition of semilattices with applications to topological lattices

Joe Bill Rhodes

Vol. 44 (1973), No. 1, 299–307

Every element with finite extent in a meet-continuous semilattice with complete chains is the meet of a finite number of meet irreducibles. This includes both semilattices with the ascending chain condition and compact topological semilattices with finite breadth. By applying this decomposition to topological lattices on an n-cell, the following results are obtained: If L and M are topological lattices on n and m-cells respectively and there is an order isomorphism between the boundaries of L and M, then L and M are homeomorphic. If, in addition, L and M are distributive, L and M are isomorphic.

Mathematical Subject Classification
Primary: 06A20
Received: 6 May 1971
Published: 1 January 1973
Joe Bill Rhodes