We consider a number of decision problems, that appear in the dynamical systems and database literature, concerning the termination of iterates of real functions. These decision problems take a function f : R n → R n as input and ask, for example, whether this function is mortal, nilpotent, terminating, or reaches a fixed point on a given point in R n . We associate topologies to functions f : R n → R n and study some basic properties of these topologies. The contribution of this paper is a translation of the above mentioned decision problems into decision problems concerning wellknown properties of topologies, e.g., connectivity. We also show that connectivity of topologies on R n is undecidable for n > 1.
['Floris Geerts', 'Bart Kuijpers']
Topological formulation of termination properties of iterates of functions