  Let X be a simplicial complex with the ground set V. Define its Alexander
dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The
combinatorial Alexander duality states that the i-th reduced homology group of
X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a
given commutative ring R). We give a self-contained proof.
