一句话：证明可计算度量空间中的半可计算图均可由端点可计算的子图任意精度逼近。
本文研究拓扑图的可计算性。拓扑图由弧和射线在端点处粘合而成。作者在可计算度量空间框架下考察半可计算图，即其点集可由半判定过程逼近的图。核心方法属于可计算分析：利用可计算子图与可计算端点的构造，对原图进行有效逼近。主要结论是：可计算度量空间中的每一个半可计算图，都能以任意精度被一个可计算子图逼近，且该子图的端点也是可计算的。这为半可计算拓扑对象与可计算对象之间的逼近关系提供了精确刻画，并拓展了可计算拓扑图理论。摘要未提供具体算法、复杂度或实验评估，结果以数学证明形式给出。
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with arbitrary precision, by its computable subgraph with computable endpoints.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{abs-2411-13672,
title = {Computable Approximations of Semicomputable Graphs},
author = {Vedran Čačić and Matea Čelar and Marko Horvat and Zvonko Iljazović},
journal = {Logical Methods in Computer Science},
volume = {Volume 22, Issue 1},
year = {2026},
doi = {10.46298/lmcs-22(1:28)2026}
}