Codimension of compact 𝑀-semilattices

Abstract

This paper is a generalization of [5] and gives a partial answer to Question 31 in [1], i.e., if S S is a compact M M -semilattice of finite codimension and x ≠ y x \ne y , then there exists a closed subsemilattice A A of S S such that A A separates x x and y y in S S and cd ⁡ A > cd ⁡ S \operatorname {cd} A > \operatorname {cd} S .