On the structure of continua with finite length and Golab's semicontinuity theorem
arXiv:1705.09941 · doi:10.1016/j.na.2016.10.012
Abstract
The main results in this note concern the characterization of the length of continua 1 (Theorems 2.5) and the parametrization of continua with finite length (Theorem 4.4). Using these results we give two independent and relatively elementary proofs of Golab's semicontinuity theorem.
23 pages, 2 figures. Compared to the previous version (which is essentially the same as the published one), we have added two pictures, corrected the proof of Lemma 2.22 and a few small mistakes, and modified the definition of δ-partition in Subsection 2.7, in order to make the statement of Proposition 2.8 stronger (consequently, we have also modified Lemma 2.18)