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arXiv · 1404.6487

Computability of 1-manifolds

Konrad Burnik·Zvonko Iljazovic
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Abstract

A semi-computable set S in a computable metric space need not be computable. However, in some cases, if S has certain topological properties, we can conclude that S is computable. It is known that if a semi-computable set S is a compact manifold with boundary, then the computability of \deltaS implies the computability of S. In this paper we examine the case when S is a 1-manifold with boundary, not necessarily compact. We show that a similar result holds in this case under assumption that S has finitely many components.

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Konrad Burnik, Zvonko Iljazovic. 2014-04-25. Computability of 1-manifolds. https://doi.org/10.2168/lmcs-10(2:8)2014

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