A partition of type $n$ on a set $X$ is a family $\Pi$ of its subsets, such that any $n$ elements of $X$ are contained in exactly one subset and every subset contains at least $n$ elements of $X$. If $X$ is a Hausdorff space and if $\Pi$ satisfies certain topological conditions (expressed by the convergence of nets) then we consider $\Pi$ as a topological space. Some examples of such partitions are given here. Topological projective and Euclidean planes appear as special cases of 2-partitions.