We examine conditions under which a semicomputable set in a computable topological space is computable. In particular, we examine topological pairs (A, B) with the following property: if X is a computable topological space and \(f:A\rightarrow X\) is an embedding such that f(A) and f(B) are semicomputable sets in X, then f(A) is a computable set in X. Such pairs (A, B) are said to have computable type. It is known that \((\mathcal {K},\{a,b\})\) has computable type if \(\mathcal {K}\) is a Hausdorff continuum chainable from a to b. It is also known that (Iⁿ, ∂Iⁿ) has computable type, where Iⁿ is the n-dimensional unit cube and ∂Iⁿ is its boundary in \(\mathbb {R}^{n} \). We generalize these results by proving the following: if \(\mathcal {K}_{i} \) is a nontrivial Hausdorff continuum chainable from a_i to b_i for \(i\in \{1,{\dots } ,n\}\), then \(({\prod }_{i=1}^{n} \mathcal {K}_{i} ,B)\) has computable type, where B is the set of all \((x_{1} ,{\dots } ,x_{n})\in {\prod }_{i=1}^{n} \mathcal {K}_{i}\) such that x_i ∈{a_i, b_i} for some \(i\in \{1,{\dots } ,n\}\).

我们研究了可计算拓扑空间中的半计算集可计算的条件。特别是，我们检查具有以下属性的拓扑对（A，B）：如果X是可计算的拓扑空间，并且\（f：A \ rightarrow X \）是一个嵌入，使得f（A）和f（B）为X中的半可计算集合，则f（A）是X中的可计算集合。此类对（A，B）具有可计算类型。已知\（（\ mathcal {K}，\ {a，b \}）\）如果\（\ mathcal {K} \）是可从a链接到b的Hausdorff连续体，则具有可计算的类型。还已知的是（我^Ñ，∂我^Ñ）具有可计算的类型，其中我^Ñ是Ñ维单位立方体和∂我^Ñ是其边界在\（\ mathbb {R} ^ {N} \） 。我们通过证明以下概括这些结果：如果\（\ mathcal {K} _ {I} \）是一个非平凡的Hausdorff连续环连接从一个_我到b_我为\（I \在\ {1，{\点}， n \} \），则\（（{{prod} _ {i = 1} ^ {n} \ mathcal {K} _ {i}，B）\）具有可计算类型，其中B是所有\（（x_ {1 }，{\点}，X_ {N}）\在{\ PROD} _ {i = 1} ^ {N} \ mathcal {K} _ {I} \），使得X_我∈{一个_我，b_我}表示\（i \ in \ {1，{\ dots}，n \} \）。