Decomposition of topologies on lattices and hyperspaces
AbstractThe notion of decomposable topology is introduced in a partially ordered set and, in particular, in the lattice C(X) of all closed subsets (ordered by reverse inclusion) of a topological space X, which is also called the hyperspace of X. This notion is closely related to the concepts, defined in the same framework, of lower, upper and strong upper topology.We investigate decomposability and unique decomposability of the main hyperspace topologies, and of topologies which are defined on some...