摘要翻译：
长期以来，空间对象拓扑信息的研究一直是计算几何、空间推理、认知科学和机器人学等学科的研究热点。虽然这些研究大多强调空间物体之间的拓扑关系，但这项工作研究的是有界平面区域的内部拓扑结构，这些区域可以由多个碎片组成和/或具有任何有限水平的孔和岛。简单区域（同胚于封闭圆盘的区域）在处理空间实体和现象的多样性和复杂性方面的不足已经得到了广泛的承认。简单区域的另一个显著缺点是，它们在集合运算并、交和差下不是封闭的。本文考虑了有界半代数区域，它在集合运算下是闭的，可以逼近实际中出现的大多数平面区域。
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英文标题：
《On the Internal Topological Structure of Plane Regions》
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作者：
Sanjiang Li
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最新提交年份：
2013
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Computational Geometry        计算几何
分类描述：Roughly includes material in ACM Subject Classes I.3.5 and F.2.2.
大致包括ACM课程I.3.5和F.2.2中的材料。
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英文摘要：
  The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches emphasised the topological relations between spatial objects, this work studies the internal topological structure of bounded plane regions, which could consist of multiple pieces and/or have holes and islands to any finite level. The insufficiency of simple regions (regions homeomorphic to closed disks) to cope with the variety and complexity of spatial entities and phenomena has been widely acknowledged. Another significant drawback of simple regions is that they are not closed under set operations union, intersection, and difference. This paper considers bounded semi-algebraic regions, which are closed under set operations and can closely approximate most plane regions arising in practice.
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PDF链接：
https://arxiv.org/pdf/0909.0109