Decompositions of cyclic elements of locally connected continua
Volume 119 / 2010
Colloquium Mathematicum 119 (2010), 321-330
MSC: Primary 54F30; Secondary 54B15, 54D05, 54F05.
DOI: 10.4064/cm119-2-10
Abstract
Let $X$ denote a locally connected continuum such that cyclic elements have metrizable $G_{\delta }$ boundary in $X$. We study the cyclic elements of $X$ by demonstrating that each such continuum gives rise to an upper semicontinuous decomposition $G$ of $X$ into continua such that $X/G$ is the continuous image of an arc and the cyclic elements of $X$ correspond to the cyclic elements of $X/G$ that are Peano continua.
