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/