Lattices with no interval homomorphisms
Jimmie Lawson · Pacific Journal of Mathematics · 1970
This paper arose from the following analogous questions: (1) Does a distributive topological lattice on a continuum admit sufficiently many continuous lattice homomorphisms onto the unit interval to separate points, and (2) does a topological semilattice on a continuum admit sufficiently many continuous semilattice homomorphisms onto the unit interval to separate points? Earlier investigations of topological lattices and semilattices have provided partial positive solutions. However, examples of an infinite-dimensional distributive lattice and a one-dimensional semilattice which admit only trivial homomorphisms into the interval are presented in this paper. © 1970 Pacific Journal of Mathematics.