Inner points and breadth in certain compact semilattices
Dennison R. Brown, James W. Stepp · Proceedings of the American Mathematical Society · 1982
A point x ∈ X x \in X is inner if there exists an open set U U containing x x such that for each open set V V with x ∈ V ⊆ U x \in V \subseteq U , the inclusion homomorphism i ∗ : {i^* }: : H ∗ ( X , X ∖ V ) → H ∗ ( X , X ∖ U ) {H^*}(X,X \setminus V) \to {H^*}(X,X \setminus U) is nontrivial. In this note it is proved that, if X X is a compact, chainwise connected topological semilattice of codimension n n , and x x is a point of breadth n + 1 n + 1 , then x x is an inner point.