= Rational summand in Hawaiian earring homology
{title2=$\mathbb Q\text{ is a direct summand of }H_1(\mathbb H;\mathbb Z)$}
The first integral <singular homology> of the <Hawaiian earring> has a <direct summand> isomorphic to $\mathbb Q$. This consequence of its structural homology theorem suffices, through the <universal coefficient theorem for cohomology> and <nonzero Ext of the rationals with integer coefficients>, to show that its integral $H^2$ is nonzero. The precise structural theorem is Theorem 3.1 of https://www.sas.rochester.edu/mth/sites/doug-ravenel/otherpapers/eda-kawamura2.pdf.
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