A characterization of the kernel of a closed set
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- by Marilyn Breen PDF
- Proc. Amer. Math. Soc. 51 (1975), 431-433 Request permission
Abstract:
Let $S$ be a closed subset of some linear topological space such that int ker $S \ne \phi$ and ker $S \ne S$ 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 $\mathfrak {M} \ne \phi$ and $\cap \mathfrak {M} = \ker S$.References
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 51 (1975), 431-433
- MSC: Primary 52A05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0372749-6
- MathSciNet review: 0372749