ℵ₁‐directed inverse systems of continuous images of arcs

Abstract

Abstract. The main purpose of this paper is to prove that if X = {X a ,p ab ,A} is a usual ℵ 1 -directed inverse system of continuous images of arcs with monotone bonding mappings, then X = lim X is a continuous image of an arc (Theorem 2.4). Some applications of this statement are also given.