Автоморфізми та ендоморфізми розбиттів топологічних просторів
Abstract
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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Mathematical Dynamics and Fractals
Geometric and Algebraic Topology
Publication details
- Journal / source
- Ukrains’kyi Matematychnyi Zhurnal
- Volume
- 78
- Issue
- 1-2
- Pages
- 47–70
- Publication date
- 27 January 2026
- Language
- UK