arXiv subjects

Zvonko Iljazovic

Publications and source records attributed to Zvonko Iljazovic.

3 recordsLinked to original sources

arXiv2014

Computability of 1-manifolds

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.

cs.LO↗

arXiv2013

Compact manifolds with computable boundaries

We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with computable boundary is computable. In fact, we examine the notion of a semi-computable compact set and we prove a more general result: in any computable metric space each semi-computable compact manifold with computable boundary is computable. In particular, each semi-computable compact (boundaryless) manifold is computable.

cs.LO↗

arXiv2011

Co-c.e. spheres and cells in computable metric spaces

We investigate conditions under which a co-computably enumerable set in a computable metric space is computable. Using higher-dimensional chains and spherical chains we prove that in each computable metric space which is locally computable each co-computably enumerable sphere is computable and each co-c.e. cell with co-c.e. boundary sphere is computable.

cs.LO↗