Kernels of Hereditarily Unicoherent Continua and Absolute Retracts
For a hereditarily unicoherent continuum X, its kernel means the common part of all subcontinua of X that intersect all arc components of X. This concept naturally appears when absolute retracts for the class of hereditarily unicoherent continua are studied. Let Y be such an absolute retract. Among other results, we prove that (a) Y is indecomposable if and only if it is identical with its kernel; (b) the dimension and the shape of Y are the same as ones of the kernel of Y ; (c) either Y is tree-like or the kernel of Y is indecomposable.
J. J. Charatonik et al., "Kernels of Hereditarily Unicoherent Continua and Absolute Retracts," Topology Proceedings, Auburn University, Jan 2001.
Mathematics and Statistics
Keywords and Phrases
absolute retract; arc approximation property; arc component; arc property of Kelley; continuum; decomposable; dendroid; hereditarily unicoherent; kernel; property of Kelley; retraction
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