A space of ideals
Solution 1:
This space is considered in this paper. For a f.g. commutative ring $R$, it determines the topological type of $\mathcal{I}(R)$.
This paper focuses on the case of a finitely generated free commutative ring, but the general case is addressed, see Section 4: it considers, more generally, the case of submodules of an $R$-module ($R$ any ring). The space of ideals of a ring is the particular case of the free module of rank 1.