We consider topological pairs $(A,B)$, $B\subseteq A$, which have computable type, which means that they have the following property: if X is a computable topological space and $f:A\to X$ a topological imbedding such that $f(A)$ and $f(B)$ are semicomputable sets in X, then $f(A)$ is a computable set in X. It is known, e.g., that $(M,\partial M)$ has computable type if M is a compact manifold with boundary. In this paper we examine topological spaces called graphs and we show that we can in a natural way associate to each graph G a discrete subspace E so that $(G,E)$ has computable type. Furthermore, we use this result to conclude that certain noncompact semicomputable graphs in computable metric spaces are computable.

中文翻译：

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图的可计算性

我们考虑拓扑对 $（\mathrm{一种}，乙）$， $乙\subseteq \mathrm{一种}$，具有可计算的类型，这意味着它们具有以下属性：如果X是可计算的拓扑空间，并且$F：\mathrm{一种}\to X$ 诸如此类的拓扑嵌入 $F（\mathrm{一种}）$ 和 $F（乙）$是X中的半计算集，则$F（\mathrm{一种}）$是X中的可计算集合。众所周知，例如$（\mathrm{中号}，\partial \mathrm{中号}）$如果M是带边界的紧流形，则为可计算类型。在本文中，我们研究了称为图的拓扑空间，并证明了我们可以自然地将每个图G关联一个离散子空间E，从而$（G，Ë）$具有可计算的类型。此外，我们使用此结果得出结论，可计算度量空间中的某些非紧致半可计算图是可计算的。