  We give an exposition of Natural Topology (NToP), which highlights its
advantages for exact computation. The NToP-definition of the real numbers (and
continuous real functions) matches recent expert recommendations for exact real
computation (see [Bauer&Kavkler2008] and [Bauer&Kavkler2009]). We retrieve
existing theory and derive strong new results on the efficient representation
of continuous real-valued functions defined on a general class of topological
spaces (called natural spaces). We then expand these results to a large class
of continuous functions between natural spaces.
