On zero dimensional sequential spaces

Abstract

We develop tools to recognize sequential spaces with large inductive dimension zero. We show the Hawaiian earring group $G$ is 0 dimensional, when endowed with the quotient topology, inherited from the space of based loops with the compact open topology. In particular $G$ is $T_4$ and hence inclusion $G \rightarrow F_M (G)$ is a topological embedding into the free topological group $F_M (G)$ in the sense of Markov.