On zero dimensional sequential spaces

Paul Fabel

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arXiv · 2007.02136

On zero dimensional sequential spaces

Paul Fabel

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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.

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BibTeX RIS

Paul Fabel. 2020-07-04. On zero dimensional sequential spaces. https://arxiv.org/abs/2007.02136

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