Is there a simple way to change the color of the region where two Points operlap?
For example in Graphics[{PointSize[2], Point[{1, 1}], Point[{0, 0}]}], the resulting two points have an area where they overlap (their union). I am looking for a simple way to make that area White, for example.

The reason I am asking is that I have a list of data points, some of which overlap. I want to show the data in a graph but I want the reader to be easily able to realize that two neighboring and overlapping points are separate. That is why I am looking for an easy way to reverse the color of their union. Points that overlap perfectly, I treat separately, by making a circle around the first point.