Fundamental groups of one-dimensional spaces

Let X be a metrizable one-dimensional continuum. In the present paper we describe the fundamental group of X as a subgroup of its Cech homotopy group. In particular, the elements of the Cech homotopy group are represented by sequences of words. Among these sequences the elements of the fundamental group are characterized by a simple stabilization condition. This description of the fundamental group is used to give a new algebro-combinatorial proof of a result due to Eda on continuity properties of homomorphisms from the fundamental group of the Hawaiian earring to that of X.