  This paper dualizes the setting of affine spaces as originally introduced by
Diers for application to algebraic geometry and expanded upon by various
authors, to show that the fundamental groups of pointed topological spaces
appear as the structures of dually affine spaces. The dual of the Zariski
closure operator is introduced, and the 1-sphere and its copowers together with
their fundamental groups are shown to be examples of complete objects with
respect to the Zariski dual closure operator.
