Exact computation over topological spaces

Abstract

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.