Let E be a Banach space, Ω a locally compact space, and μ a positive Radon measure on Ω. In this paper, through extending to Lebesgue-Bochner spaces, we show that the topology β1 introduced by Singh is a type of strict topology. We then investigate various properties of this locally convex topology. In particular, we show that the strong dual of L1(μ, E) can be identified with a Banach space. We also show that the topology β1 is a metrizable, barrelled or bornological space if and only if Ω is compact. Finally, we consider the generalized group algebra under certain natural locally convex topologies. As an application of our results, we prove that under the topology β1 is a complete semi-topological algebra.