Definition 4.1.7 (Locally Convex Space).label Let $E$ be a TVS over $\curl{\R,\com}$ then $E$ is a locally convex space if there exists a family of seminorms $\curl{\rho_i}_{i\in I}$ that induces the topology on $E$
Definition 4.1.7 (Locally Convex Space).label Let $E$ be a TVS over $\curl{\R,\com}$ then $E$ is a locally convex space if there exists a family of seminorms $\curl{\rho_i}_{i\in I}$ that induces the topology on $E$