Finitely presented condensed groups

Let G G denote the space of finitely generated marked groups. For any finitely generated group G G , we construct a continuous, injective map f f from the space of subgroups S u b ( G ) Sub(G) to G G that sends conjugate subgroups to isomorphic marked groups; in addition, if G G is finitely presented and H ≤ G H≤ G is finitely generated, then f ( H ) f(H) is finitely presented. This result allows us to transfer various topological phenomena occurring in S u b ( G ) Sub(G) to G G . In particular, we provide the first example of a finitely presented group whose isomorphism class in G G has no isolated points.