The paper deals with locally connected continua in the Euclidean plane. Theorem 1 asserts that there exists a simple closed curve in that separates two given points , of if there is a subset of (a point or an arc) with this property. In Theorem 2 the two points , are replaced by two closed and connected disjoint subsets , . Again – under some additional preconditions – the existence of a simple closed curve disconnecting and is stated.
@article{701647,
title = {Disconnections of plane continua},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {2000},
pages = {53-55},
mrnumber = {MR1758078},
zbl = {0995.53003},
url = {http://dml.mathdoc.fr/item/701647}
}
Bajguz, W. Disconnections of plane continua, dans Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books, (2000), pp. 53-55. http://gdmltest.u-ga.fr/item/701647/