  Topological fixpoint logics are a family of logics that admits topological
models and where the fixpoint operators are defined with respect to the
topological interpretations. Here we consider a topological fixpoint logic for
relational structures based on Stone spaces, where the fixpoint operators are
interpreted via clopen sets. We develop a game-theoretic semantics for this
logic. First we introduce games characterising clopen fixpoints of monotone
operators on Stone spaces. These fixpoint games allow us to characterise the
semantics for our topological fixpoint logic using a two-player graph game.
Adequacy of this game is the main result of our paper. Finally, we define
bisimulations for the topological structures under consideration and use our
game semantics to prove that the truth of a formula of our topological fixpoint
logic is bisimulation-invariant.
