| 韩景銮.次线性泛函与分离定理[J].数学研究及应用,1984,4(2):97~98 |
| 次线性泛函与分离定理 |
| Sublinear Functional and Separation Theorem |
| 投稿时间：1982-09-06 |
| DOI：10.3770/j.issn:1000-341X.1984.02.023 |
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| In this note, we consider a family of functional S={pV|V∈U} , where U is a local base of a locally convex topological linear space (E,T) consisting of all convex neighbourhoods of θ, pV is the Minkowski's functional of V. It is proved that the family S can distinguishes compact convex set and bounded closed convex set. In the sequel, an elementary proof of H. Bauer's maximality principle and Krein-Milman theorem are given. Some other interesting properties of s are given also. |
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