Pairwise disjoint refinements of coverings of one-dimensional Peano continua
Keywords:
one-dimensional, Peano continua, refinement, disjointAbstract
For a given finite open cover $\mathcal{O}$ of a one-dimensional Peano continuum $X$, there exist refinements $\mathcal{O}_0$ and $\mathcal{O}_1$ of $\mathcal{O}$ consisting of connected open sets such that $\mathcal{O}_0 \cup \mathcal{O}_1$ covers $X$ and both $\mathcal{O}_0$ and $\mathcal{O}_1$ are pairwise disjoint families.
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