On Topology of Three-dimensional Continua with Singular Points
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911311178235904 |
|---|---|
| author | Liang, Hao Qiu, Yunhao Tan, Yan Zhang, Qinghai |
| author_facet | Liang, Hao Qiu, Yunhao Tan, Yan Zhang, Qinghai |
| contents | We propose to model the topology of three-dimensional (3D) continua by Yin sets, regular open semianalytic sets with bounded boundary. Our model differs from manifold-based models in that singular points of a 3D continuum, i.e., boundary points where the tangent plane is not uniquely defined, are treated not as anomalies but as a central subject of our theoretical investigation. We characterize the local and global topology of Yin sets. Then we give a unique boundary representation of Yin sets based on the notion of a glued surface, a quotient space of an orientable compact 2-manifold along a one-dimensional CW complex. Our results apply to 3D continua with arbitrarily complex topology and may be useful in a number of scientific and engineering applications such as solid modeling, computer-aided design, and numerical simulations of multiphase flows with topological changes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Topology of Three-dimensional Continua with Singular Points Liang, Hao Qiu, Yunhao Tan, Yan Zhang, Qinghai Geometric Topology 76T99, 68U07, 74A50 We propose to model the topology of three-dimensional (3D) continua by Yin sets, regular open semianalytic sets with bounded boundary. Our model differs from manifold-based models in that singular points of a 3D continuum, i.e., boundary points where the tangent plane is not uniquely defined, are treated not as anomalies but as a central subject of our theoretical investigation. We characterize the local and global topology of Yin sets. Then we give a unique boundary representation of Yin sets based on the notion of a glued surface, a quotient space of an orientable compact 2-manifold along a one-dimensional CW complex. Our results apply to 3D continua with arbitrarily complex topology and may be useful in a number of scientific and engineering applications such as solid modeling, computer-aided design, and numerical simulations of multiphase flows with topological changes. |
| title | On Topology of Three-dimensional Continua with Singular Points |
| topic | Geometric Topology 76T99, 68U07, 74A50 |
| url | https://arxiv.org/abs/2512.02385 |