In this page, in abstract, it is claimed that the poset of all Hausdorff precompact group topologies on an abelian group $G$, is order-isomorphic to the the subgroup lattice of $\hat{G}$, the character group of $G$.

What is where, on the internet, can I find a proof for this claim?

If this is the correct version of the claim, for an infinite abelian group $G$, we must have $|\hat{G}|=2^{2^{|G|}}$. Is this correct?

In this page, in abstract, it is claimed that the poset of all Hausdorff precompact group topologies on an abelian group $G$, is order-isomorphic to the the subgroup lattice of $\hat{G}$, the character group of $G$.

What is or where, on the internet, can I find a proof for this claim?

If this is the correct version of the claim, for an infinite abelian group $G$, we can have $|\hat{G}|=2^{2^{|G|}}$. Is this correct?

In this page, in abstract, it is claimed that the poset of all Hausdorff precompact group topologies on an abelian group $G$, is order-isomorphic to the the subgroup lattice of $\hat{G}$, the charater group of $G$.

What is where, on the internet, can I find a proof for this claim?

If this is the correct version of the claim, for an infinite abelian group $G$, we must have $|\hat{G}|=2^{2^{|G|}}$. Is this correct?

In this page, in abstract, it is claimed that the poset of all Hausdorff precompact group topologies on an abelian group $G$, is order-isomorphic to the the subgroup lattice of $\hat{G}$, the character group of $G$.

What is where, on the internet, can I find a proof for this claim?

If this is the correct version of the claim, for an infinite abelian group $G$, we must have $|\hat{G}|=2^{2^{|G|}}$. Is this correct?