Let X be a one-dimensional Peano continuum. Then the singular homology group H₁(X) is isomorphic to a free abelian group of finite rank or the singular homology group of the Hawaiian earring.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-2-1, author = {K. Eda}, title = {Singular homology groups of one-dimensional Peano continua}, journal = {Fundamenta Mathematicae}, volume = {233}, year = {2016}, pages = {99-115}, zbl = {1335.55005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-2-1} }
K. Eda. Singular homology groups of one-dimensional Peano continua. Fundamenta Mathematicae, Tome 233 (2016) pp. 99-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-2-1/