We consider random samples in $\mathbb{R}^d$ drawn from an unknown density. This paper is devoted to the study the properties of the Delaunay polyhedron restricted to nearest neighbors as an estimator of the density support preserving its topological properties. When the dimension of the support is $d$, we exhibit suitable value for the number of neighbors to be used. This value ensure that, when $d=2$, our estimator is a.a.s.\/ homeomorph to the support. Empirically, our estimator also preserves the topology for higher dimensions but it is not proved here. When $f$ is Lipschitz continuous and the boundary of $S$ is smooth the value depends on $d$ and the size of the sample only. The convergence of the underlying estimator to the support is proved and a lower bound for the convergence rate is given. When the dimension of the support is less than $d$, another estimator is proposed.
