Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.15696 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911452283011072 |
|---|---|
| author | Kubiś, Wiesław Kucharski, Andrzej Turek, Sławomir |
| author_facet | Kubiś, Wiesław Kucharski, Andrzej Turek, Sławomir |
| contents | We study the properties of a generic object $\mathbb{P}$ in the category of finite graphs. It turns out that this object, being topologically a Cantor set, has the Knaster--Reichbach type property. Namely, every homeomorphism and isomorphism $h\colon K\to L$ where $K$ and $L$ are nowhere dense closed sets in $\mathbb{P}$ and consisting only of isolated vertices in $K$ and $L$ can be extended to the autohomeomorphism and autoisomorphism of the whole graph $\mathbb{P}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15696 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Knaster--Reichbach type theorem for graph structures Kubiś, Wiesław Kucharski, Andrzej Turek, Sławomir General Topology Category Theory 54B30, 05C63, 18F60, 54C25, 54C15 We study the properties of a generic object $\mathbb{P}$ in the category of finite graphs. It turns out that this object, being topologically a Cantor set, has the Knaster--Reichbach type property. Namely, every homeomorphism and isomorphism $h\colon K\to L$ where $K$ and $L$ are nowhere dense closed sets in $\mathbb{P}$ and consisting only of isolated vertices in $K$ and $L$ can be extended to the autohomeomorphism and autoisomorphism of the whole graph $\mathbb{P}$. |
| title | A Knaster--Reichbach type theorem for graph structures |
| topic | General Topology Category Theory 54B30, 05C63, 18F60, 54C25, 54C15 |
| url | https://arxiv.org/abs/2602.15696 |