Locally hulled topologies

We present a general result about generating group topologies by pseudo-norms. Namely, we show that if a topology has a base of sets which are closed in a certain sense, then it can be generated by a collection of pseudo-norms such that the balls in these pseudo-norms are also closed in the same sense. The examples include linear and locally convex topologies on vector spaces, locally solid and Fatou topologies on vector lattices and Fréchet-Nikodým topologies on Boolean algebras.