MCS Spaces are CS
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913176988155904 |
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| author | Alattar, Mohammad Tadman, Lewis |
| author_facet | Alattar, Mohammad Tadman, Lewis |
| contents | In this paper we further develop the theory of MCS spaces. Our main result shows that MCS spaces, as defined by Perelman, are CS sets with respect to their MCS stratification, and that in fact, the intrinsic stratification agrees with the MCS stratification. As a consequence, we improve on Perelman's result and answer affirmatively a question by Fujioka. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01119 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | MCS Spaces are CS Alattar, Mohammad Tadman, Lewis Geometric Topology General Topology Metric Geometry 57N16, 57N80, 53C23 In this paper we further develop the theory of MCS spaces. Our main result shows that MCS spaces, as defined by Perelman, are CS sets with respect to their MCS stratification, and that in fact, the intrinsic stratification agrees with the MCS stratification. As a consequence, we improve on Perelman's result and answer affirmatively a question by Fujioka. |
| title | MCS Spaces are CS |
| topic | Geometric Topology General Topology Metric Geometry 57N16, 57N80, 53C23 |
| url | https://arxiv.org/abs/2606.01119 |