A metric condition which implies dimension ≤1

Source abstract

A class of 1 1 -dimensional spaces is distinguished by special type embeddings in compacta, or a corresponding metric property. In this setting, a simple proof of the Oversteegen-Tymchatyn theorem that the spaces of homeomorphisms of the Sierpiński’s Carpet and the Menger Universal Curve have dimension ≤ 1 \leq 1 is given.