On the structure of homeomorphisms of the open annulus

Lucien Guillou

Displaying similar documents to “On the structure of homeomorphisms of the open annulus”

Disconnections of plane continua

Bajguz, W.

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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.