Autohomeomorphisms of pre-images of $\mathbb N^*$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929385265692672 |
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| author | Dow, Alan |
| author_facet | Dow, Alan |
| contents | In the study of the Stone-uCech remainder of the real line a detailed study of the Stone-uCech remainder of the space $\mathbb N\times [0,1]$, which we denote as $\mathbb M$, has often been utilized. Of course the real line can be covered by two closed sets that are each homeomorphic to $\mathbb M$. It is known that an autohomeomorphism of $\mathbb M^*$ induces an autohomeomorphism of $\mathbb N^*$. We prove that it is consistent with there being non-trivial autohomeomorphism of $\mathbb N^*$ that those induced by autohomeomorphisms of $\mathbb M^*$ are trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Autohomeomorphisms of pre-images of $\mathbb N^*$ Dow, Alan General Topology 54A35 In the study of the Stone-uCech remainder of the real line a detailed study of the Stone-uCech remainder of the space $\mathbb N\times [0,1]$, which we denote as $\mathbb M$, has often been utilized. Of course the real line can be covered by two closed sets that are each homeomorphic to $\mathbb M$. It is known that an autohomeomorphism of $\mathbb M^*$ induces an autohomeomorphism of $\mathbb N^*$. We prove that it is consistent with there being non-trivial autohomeomorphism of $\mathbb N^*$ that those induced by autohomeomorphisms of $\mathbb M^*$ are trivial. |
| title | Autohomeomorphisms of pre-images of $\mathbb N^*$ |
| topic | General Topology 54A35 |
| url | https://arxiv.org/abs/2406.09319 |