Taylor.md

Title. Some two-dimensional lattices that fail distributivity or fail modularity and some other laws

Author. Walter Taylor

Institution. Mathematics Department, University of Colorado, Boulder

Abstract. For $$L$$ a finite simple lattice, we can examine the class of topological spaces that can support a lattice (with continuous operations) that admits $$L$$ as a 0,1-sublattice. We consider this problem for various modular $$L$$, such as $$M_n$$ ($$n\geq 3$$) and possibly $$M_{p,q}$$. Also a brief look at the distributive case. So far our spaces are small finite geometric examples, very user-friendly.