Disconnections of plane continua. (English) Zbl 0995.53003

Slovák, Jan (ed.) et al., The proceedings of the 19th Winter School “Geometry and physics”, Srní, Czech Republic, January 9-15, 1999. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 63, 53-55 (2000).
The paper deals with locally connected continua \(X\) in the Euclidean plane. Theorem 1 asserts that there exists a simple closed curve in \(X\) that separates two given points \(x\), \(y\) of \(X\) if there is a subset \(L\) of \(X\) (a point or an arc) with this property. In Theorem 2 the two points \(x\), \(y\) are replaced by two closed and connected disjoint subsets \(A\), \(B\). Again – under some additional preconditions – the existence of a simple closed curve disconnecting \(A\) and \(B\) is stated.
For the entire collection see [Zbl 0940.00040].
Reviewer: Johann Lang (Graz)


53A04 Curves in Euclidean and related spaces
54D05 Connected and locally connected spaces (general aspects)