Computability of 1-manifolds
Logic in Computer Science
2015-07-01 v2 Logic
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.
Keywords
Cite
@article{arxiv.1404.6487,
title = {Computability of 1-manifolds},
author = {Konrad Burnik and Zvonko Iljazovic},
journal= {arXiv preprint arXiv:1404.6487},
year = {2015}
}