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/