Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat