On P-simple points

A simple point of an object is a point whose removal does not change the topology. However, the simultaneous deletion of simple points may change the topology. A popular way for overcoming this problem is to use a directional strategy. This method has good properties in two-dimensional discrete spaces but it does not work in three-dimensions. Through the notion of P-simple point we propose a general strategy for removing points in parallel without altering the topology of a 3D space. We also propose a characterization of P-simple points which may be implemented with a linear time complexity