Exact computation over topological spaces
General Topology
2018-06-06 v1 Logic
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.
Cite
@article{arxiv.1806.01636,
title = {Exact computation over topological spaces},
author = {Frank Waaldijk},
journal= {arXiv preprint arXiv:1806.01636},
year = {2018}
}
Comments
31 pages, originally submitted to LMCS in 2013, rejected in 2017 (no communication in between). arXiv admin note: substantial text overlap with arXiv:1210.6288