We investigate under what conditions a co-recursively enumerable set S in a computable metric space (X, d, Î±) is recursive. The topological properties of S play an important role in view of thisâ€¦ (More)

We investigate the relationship between computable metric spaces (X, d, Î±) and (X, d, Î²), where (X, d) is a given metric space. In the case of Euclidean space, Î± and Î² are equivalent up to isometry,â€¦ (More)

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 eachâ€¦ (More)

We examine co-c.e. sets with disconnected complements in a computable metric space. We focus on the case when the computable metric space is effectively locally connected and when the connectedâ€¦ (More)

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 computableâ€¦ (More)

Article history: Received 7 April 2016 Received in revised form 9 July 2016 Accepted 11 October 2016 Available online xxxx MSC: 03D78 03F60 68Q05 57N99

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 ifâ€¦ (More)