## 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)

### MSC:

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