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Title: Disconnections of plane continua (English)
Author: Bajguz, W.
Language: English
Journal: Proceedings of the 19th Winter School "Geometry and Physics"
Issue: 1999
Pages: 53-55
Category: math
Summary: 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. (English)
MSC: 53A04
MSC: 54D05
MSC: 54F15
idZBL: Zbl 0995.53003
idMR: MR1758078
Date available: 2009-07-13T21:42:52Z
Last updated: 2012-09-18
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