A mechanical proof of the C. T. Yang's Theorem related to a property of derived sets in general topology

Zhengfeng, Yang; Wang, Jianlin; Kobayashi, Hiroki; Zeng, Zhenbing

doi:10.1360/ssm-2019-0301

Cited by 1 publication

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References 6 publications

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“…In the research process of two-dimensional spatial data model, many scientists have discussed the definition of two-dimensional space and spatial entities from different perspectives, such as spatial data organization, expression of spatial relations between objects, and data integrity constraints. Among them, the representative system is the topological unit structure theory proposed by Corbett and Whito [1], that is, the topological theory and graph theory on two-dimensional Euclidean space are used to explain and describe two-dimensional spatial entities and the spatial relations between entities. In this method, the real world is abstractly expressed as a 2D Planar Graphs G -(v, R).…”

Section: Introductionmentioning

confidence: 99%

Formal topological description of three-dimensional topological entities based on k-dimensional pseudo-manifold

Zhao

2023

TNS

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This paper clarifies the necessity of studying three-dimensional spatial data models, analyzes the research progress and existing problems of topological spatial relationship description methods, and proposes a complete and formal description framework of three-dimensional topological spatial relations based on point set topological theory and dimension expansion method. On this basis, the topological spatial relations existing in three-dimensional spatial objects are classified, and five fundamental topological spatial relations are defined. The mutual exclusivity and completeness of the minimal set of 3D topological space relations are proved. Based on point set topology and k-dimensional pseudo-manifold, this paper proposes the formal description of three-dimensional topological properties and spatial relations between spatial entities. The simplicial homology is applied to manifolds, the topological properties of three-dimensional space entities are revealed, and the formal description method of three-dimensional space entities is given through the geometric structural relationship between simplex and simplicial k-complex.

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Section: Introductionmentioning

confidence: 99%