Relatively Uniformly Continuous Semigroups on Vector Lattices

In this paper we study continuous semigroups of positive operators on general vector lattices equipped with the relative uniform topology \(\tau_{ru}\). We introduce the notions of strong continuity with respect to \(\tau_{ru}\) and relative uniform continuity for semigroups. These notions allow us to study semigroups on non-locally convex spaces such as \(L^p(\mathbb{R})\) for \(0