| 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. |
