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Displaying similar documents to “Some classes of locally connected continua”

On partitions in cylinders over continua and a question of Krasinkiewicz

Mirosława Reńska (2011)

Colloquium Mathematicae

Similarity:

We show that a metrizable continuum X is locally connected if and only if every partition in the cylinder over X between the bottom and the top of the cylinder contains a connected partition between these sets. J. Krasinkiewicz asked whether for every metrizable continuum X there exists a partiton L between the top and the bottom of the cylinder X × I such that L is a hereditarily indecomposable continuum. We answer this question in the negative. We also present a...

Local connectivity, open homogeneity and hyperspaces.

J. J. Charatonik (1993)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua...