A Characterization of the Kernel of a Closed Set
Marilyn Breen · Proceedings of the American Mathematical Society · 1975
Let $S$ be a closed subset of some linear topological space such that int ker $S e \phi$ and ker $S e S$ Let $\mathcal {C}$ denote the collection of all maximal convex subsets of $S$ and, for any fixed $k \geq 1$, let $\mathfrak {M} = \{ {A_1} \cup \cdots \cup {A_k}:{A_1}, \ldots ,{A_k}$ distinct members of $\mathcal {C}\}$. Then $\mathfrak {M} e \phi$ and $\cap \mathfrak {M} = \ker S$.