Kernels of hereditarily unicoherent continua and absolute retracts by Janusz J. Charatonik, W{\l}odzimierz J. Charatonik and Janusz R. Prajs

Topology Proceedings 26 No. 1 (2001-2002), pp. 127-145

Kernels of hereditarily unicoherent continua and absolute retracts

Janusz J. Charatonik, Wlodzimierz J. Charatonik and Janusz R. Prajs

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.

Keywords: absolute retract, arc approximation property, arc component, arc property of Kelley, continuum, decomposable, dendroid, hereditarily unicoherent, kernel, property of Kelley, retraction
Mathematics Subject Classification: 54F15 54F50 (54C55)

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Topology Proceedings, Volume 26 No. 1 (2001-2002)
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