Preserving topological properties of binary objects during thinning procedures is an important issue in the field of image analysis. In this context, we present the new notion of simple set which extends the well-known notion of simple point. Similarly to simple points, simple sets have the property that the homotopy type of the object in which they lie is not changed when such sets are removed. This paper defines and justifies the concept of simple sets and of a sub-family of such sets called minimal simple sets. It also briefly describes some first results and work in progress on this subject.