English

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}
}
R2 v1 2026-06-22T03:58:50.689Z