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Exact computation over topological spaces

By Frank Waaldijk

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.Comment: 31 pages, originally submitted to LMCS in 2013, rejected in 2017 (no communication in between). arXiv admin note: substantial text overlap with arXiv:1210.628

Topics: Mathematics - General Topology, Mathematics - Logic, 54A99, 54B99, 54C05, 54C10, 65G99, 03D78, 03D99, 26E40, 03F60
Year: 2018
OAI identifier: oai:arXiv.org:1806.01636

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