Disconnections of plane continua
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.