# semi-norm determines locally convex topological vector space

Consider a locally convex topological vector space. Now, using Minkowski functional (which are semi-norms) we can define a family of semi-norms indexed by the local basis (convex,balanced, absorbing) of the locally convex topological vector space. Now they can be used to define a topology and a locally convex topological vector space. How do I check that the new topology is same as the old one ?