2 problems

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Nonexistence of the Mackey topology for general locally quasi-convex groups
Let $(G,\tau)$ be an abelian topological group, let $G^\wedge$ be its dual group, and consider the locally quasi-convex group topologies on $G$ whose dual group is $G^\wedge$ ; thes…
Conjectureopenlocally-quasi-convex-groups mackey-topology topological-groupsarXiv posted 2 days ago
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The metrizable locally quasi-convex Mackey group conjecture
Metrizable LQC Mackey conjecture. Every metrizable $(G,\mu)\in \operatorname{LCS}$ is a Mackey group in $\operatorname{LQC}$ .
Conjectureopenlocally-quasi-convex-groups mackey-topology topological-groupsarXiv posted 2 days ago

Nonexistence of the Mackey topology for general locally quasi-convex groups