Contrary to a statement of Borsuk the author proves that every locally plane Peano continuum is embeddable into a 2-manifold.
@article{701669, title = {On embedding curves in surfaces}, booktitle = {Proceedings of the 20th Winter School "Geometry and Physics"}, series = {GDML\_Books}, publisher = {Circolo Matematico di Palermo}, address = {Palermo}, year = {2001}, pages = {83-96}, mrnumber = {MR1826681}, zbl = {0977.54026}, url = {http://dml.mathdoc.fr/item/701669} }
Bajguz, W. On embedding curves in surfaces, dans Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books, (2001), pp. 83-96. http://gdmltest.u-ga.fr/item/701669/