We show that each of the classes of hereditarily locally connected, finitely Suslinian, and Suslinian continua is Π₁¹-complete, while the class of regular continua is Π₀⁴-complete.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm182-1-4, author = {Udayan B. Darji and Alberto Marcone}, title = {Complexity of curves}, journal = {Fundamenta Mathematicae}, volume = {184}, year = {2004}, pages = {79-93}, zbl = {1059.03046}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm182-1-4} }
Udayan B. Darji; Alberto Marcone. Complexity of curves. Fundamenta Mathematicae, Tome 184 (2004) pp. 79-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm182-1-4/