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.