Generically hereditarily equivalent continua and topological characterization of generic maximal chains of generalized Ważewski dendrites
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912275814678528 |
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| author | Silva, Bryant Rosado Vejnar, Benjamin |
| author_facet | Silva, Bryant Rosado Vejnar, Benjamin |
| contents | The notion of hereditarily equivalent continua is classical in continuum theory with only two known nondegenerate examples (arc, and pseudoarc). In this paper we introduce generically hereditarily equivalent continua, i.e. continua which are homeomorphic to comeager many subcontinua. We investigate this notion in the realm of Peano continua and we prove that all the generalized Ważewski dendrites are such. Consequently, we study maximal chains consisting of subcontinua of generalized Ważewski dendrites and we prove that there is always a generic orbit under the homeomorphism group action. As a part of the proof we provide a topological characterization of the generic maximal chain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generically hereditarily equivalent continua and topological characterization of generic maximal chains of generalized Ważewski dendrites Silva, Bryant Rosado Vejnar, Benjamin General Topology 54F16 (primary), 54F50, 37B45 (secondary) The notion of hereditarily equivalent continua is classical in continuum theory with only two known nondegenerate examples (arc, and pseudoarc). In this paper we introduce generically hereditarily equivalent continua, i.e. continua which are homeomorphic to comeager many subcontinua. We investigate this notion in the realm of Peano continua and we prove that all the generalized Ważewski dendrites are such. Consequently, we study maximal chains consisting of subcontinua of generalized Ważewski dendrites and we prove that there is always a generic orbit under the homeomorphism group action. As a part of the proof we provide a topological characterization of the generic maximal chain. |
| title | Generically hereditarily equivalent continua and topological characterization of generic maximal chains of generalized Ważewski dendrites |
| topic | General Topology 54F16 (primary), 54F50, 37B45 (secondary) |
| url | https://arxiv.org/abs/2409.16740 |