engleski

Topological Rays and Lines as co-c.e. Sets

A co-computably enumerable 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. There are some results which give such properties in the case when $S$ is compact. In this paper we consider the following (noncompact) case: $S$ is homeomorphic to $\mathbb{; ; R}; ; $ or $[0, \infty\rangle $. More generally, we consider the case when $S$ is a (noncompact) 1-manifold with boundary.

computable metric space; computable set; co-c.e. set; topological ray; topological line

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