Pairwise disjoint refinements of coverings of one-dimensional Peano continua - Eda, Katsuya; Meilstrup, Mark (Topology Proceedings, 2023)
For a given finite open cover O of a one-dimensional Peano continuum X, there exist refinements O_0 and O_1 of O consisting of connected open sets such that O_0 O_1 covers X and both O_0 and O_1 are pairwise disjoint families.