
TL;DR
This paper develops tools to identify zero-dimensional sequential spaces and demonstrates that the Hawaiian earring group, with a specific topology, is zero-dimensional and embeds into a free topological group, revealing new structural properties.
Contribution
It introduces methods to recognize zero-dimensional sequential spaces and proves the Hawaiian earring group is zero-dimensional and embeds into a free topological group.
Findings
Hawaiian earring group is 0-dimensional with the quotient topology.
The group is $T_4$ and embeds into the free topological group $F_M(G)$.
Tools for recognizing zero-dimensional sequential spaces are developed.
Abstract
We develop tools to recognize sequential spaces with large inductive dimension zero. We show the Hawaiian earring group is 0 dimensional, when endowed with the quotient topology, inherited from the space of based loops with the compact open topology. In particular is and hence inclusion is a topological embedding into the free topological group in the sense of Markov.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology
