  One of the main goals of region-based theories of space is to formulate a
geometrically appealing definition of points. The most famous definition of
this kind is probably due to Whitehead. However, to conclude that the objects
defined are points indeed, one should show that they are points of a
geometrical or a topological space. So far, this part of Whitehead's theory was
missing: no spaces of Whitehead points have ever been constructed. This paper
intends to fill this gap via demonstration of how the development of duality
theory for Boolean and Boolean contact algebras lets us show that Whitehead's
method of extensive abstraction offers a~construction of objects that are
fundamental building blocks of specific topological spaces.
