Preserving topological properties of objects during thinning procedures is an important issue in the field of image analysis. In the case of 2-D digital images (i.e. images defined on Z^2) such procedures are usually based on the notion of simple point. By opposition to the case of spaces of higher dimensions (i.e. Z^n, n ≥ 3), it was proved in the 80’s that the exclusive use of simple points in Z^2 was indeed sufficient to develop thinning procedures providing an output that is minimal with respect to the topological characteristics of the object. Based on the recently introduced notion of minimal simple set (generalising the notion of simple point), we establish new properties related to topology-preserving thinning in 2-D spaces which extend, in particular, this classical result to more general spaces (the 2-D pseudomanifolds) and objects (the 2-D cubical complexes).