  As an attempt to uncover the topological nature of composition of strategies
in game semantics, we present a ``topological'' game for Multiplicative
Additive Linear Logic without propositional variables, including cut moves. We
recast the notion of (winning) strategy and the question of cut elimination in
this context, and prove a cut elimination theorem. Finally, we prove soundness
and completeness. The topology plays a crucial role, in particular through the
fact that strategies form a sheaf.
