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Decompositions of cyclic elements of locally connected continua

D. Daniel (2010)

Colloquium Mathematicae

Let X denote a locally connected continuum such that cyclic elements have metrizable G δ 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.

Disconnectedness properties of hyperspaces

Rodrigo Hernández-Gutiérrez, Angel Tamariz-Mascarúa (2011)

Commentationes Mathematicae Universitatis Carolinae

Let X be a Hausdorff space and let be one of the hyperspaces C L ( X ) , 𝒦 ( X ) , ( X ) or n ( X ) ( n a positive integer) with the Vietoris topology. We study the following disconnectedness properties for : extremal disconnectedness, being a F ' -space, P -space or weak P -space and hereditary disconnectedness. Our main result states: if X is Hausdorff and F X is a closed subset such that (a) both F and X - F are totally disconnected, (b) the quotient X / F is hereditarily disconnected, then 𝒦 ( X ) is hereditarily disconnected. We also...

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