# On the structure of continua with finite length and Golab's semicontinuity theorem

## TL;DR

This paper characterizes the length of continua and their parametrization, providing elementary proofs of Golab's semicontinuity theorem, thus advancing the understanding of continuum structures with finite length.

## Contribution

It offers new characterizations and parametrizations of continua with finite length, along with elementary proofs of Golab's semicontinuity theorem.

## Key findings

- Characterization of the length of continua
- Parametrization of continua with finite length
- Elementary proofs of Golab's semicontinuity theorem

## 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.