Cylindrical Algebraic Decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic optimizations in CAD construction, robot motion planning, and the algorithmic study of the topology of semi-algebraic sets. In this paper, we construct explicit examples of CADs and CAD cells that refute several conjectures and open questions of J. H. Davenport, A. Locatelli, and G. K. Sankaran concerning these topological assumptions.

翻译：具备附加拓扑性质的柱形代数分解（CAD）已在其原始逻辑设定之外获得应用，包括CAD构造中的算法优化、机器人运动规划以及半代数集拓扑结构的算法研究。本文通过构造具体的CAD及CAD胞腔实例，反驳了J. H. Davenport、A. Locatelli与G. K. Sankaran关于这些拓扑假设的若干猜想与开放性问题。