Data discrimination after clustering
If your definition of points belonging to a cluster is simply the points closest the cluster centroid, then the boundaries cannot overlap. The point assignments are a Voronoi map like:



(Source: https://www.quora.com/What-is-the-difference-between-K-Means-and-Voronoi/answer/Ethan-Brooks-3)

The closest centroid, and thus assignment, is unambiguous.