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A locally quasi-convex abelian group without a Mackey group topology
We give the first example of a locally quasi-convex (even countable reflexive and $k_\omega$) abelian group $G$ which does not admit the strongest compatible locally quasi-convex group topology. Our group $G$ is the Graev free abelian group $A_G(\mathbf {s})$ over a convergent sequence $\mathbf {s}$.