Automorphisms and endomorphisms of partitions of topological spaces - Maksymenko, S.; Polulyakh, E. (Ukrains’kyi Matematychnyi Zhurnal, 2026)
UDC 515.1 Let X be a topological space, let Δ be a partition of X, and let Y =X/Δ be a quotient space with the corresponding quotient topology. Then the automorphism group H(Δ) of Δ (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 ψH(Δ) → 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.