2 problems

Finest precompact topology conjecture. If for $(G,\nu)$ there exists the $\operatorname{MAP}$-Mackey topology associated with $\nu$, then $\nu$ is the finest precompact group topol…

Discreteness conjecture. If $G\in \operatorname{MAP}$ is a Mackey group in $\operatorname{MAP}$, then $G$ is a discrete group.