The free locally convex space $L(\mathbf{s})$ over a convergent sequence $\mathbf{s}$ is not a Mackey space

Abstract

We show that the free locally convex space $L(\mathbf{s})$ over a convergent sequence $\mathbf{s}$ is not a Mackey space. Consequently $L(\mathbf{s})$ is not a Mackey group that answers negatively a question posed in [4].