Automorphisms and endomorphisms of partitions of topological spaces
UDC 515.1 Let $X$ be a topological space, let $\Delta$ be a partition of $X$, and let $Y =X/\Delta$ be a quotient space with the corresponding quotient topology. Then the automorphism group $\mathcal{H}(\Delta)$ of $\Delta$ (i.e., the homeomorphisms of $X,$ which permute the elements of partition) ...
Збережено в:
| Дата: | 2026 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8932 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 515.1
Let $X$ be a topological space, let $\Delta$ be a partition of $X$, and let $Y =X/\Delta$ be a quotient space with the corresponding quotient topology. Then the automorphism group $\mathcal{H}(\Delta)$ of $\Delta$ (i.e., the homeomorphisms of $X,$ which permute the elements of partition) acts in a natural way upon $Y$ by homeomorphisms. We determine the cases in which the corresponding homomorphism of the action $\psi\colon\mathcal{H}(\Delta) \to \mathcal{H}(Y)$ into the group of homeomorphisms of $Y$ is continuous with respect to the compact-open topologies. The obtained results have applications to the foliation theory. |
|---|---|
| DOI: | 10.3842/umzh.v78i1-2.8932 |