A characterization of compact connected planar lattices
Charles W. Clark, Carl Eberhart · Pacific Journal of Mathematics · 1968
In this paper it is proved that every topological lattice on the two-cell is topologically isomorphic (iseomorphic) to a sublattice of the product lattice I X I.An explicit description of the compact connected sublattices of I X J containing (0, 0) and (1,1) is given.These results, together with a theorem of A. D. Wallace, yield a characterization of all compact connected lattices in the plane: each is iseomorphic to a sublattice of I X I.