A characterization of continuous images of arcs by their images of weight $leqaleph_1$

The main purpose of this paper is to characterize the continuous images of arcs by their images of the weight $leqaleph_1$. More precisely, we will show that a compact space X is the continuous image of an arc if and only if every continuous image Y = f(X) with w(Y)$leqaleph_1$ is a continuous image of an arc