Displaying similar documents to “On a family of dendrites.”

An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic

Pavel Pyrih (1999)

Commentationes Mathematicae Universitatis Carolinae

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Such spaces in which a homeomorphic image of the whole space can be found in every open set are called . W.J. Charatonik and A. Dilks asked if any strongly self-homeomorphic dendrite is pointwise self-homeomorphic. We give a negative answer in Example 2.1.

On open light mappings

Władysław Makuchowski (1994)

Commentationes Mathematicae Universitatis Carolinae

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Whyburn has proved that each open mapping defined on arc (a simple closed curve) is light. Charatonik and Omiljanowski have proved that each open mapping defined on a local dendrite is light. Theorem 3.8 is an extension of these results.

AANR spaces and absolute retracts for tree-like continua

Janusz Jerzy Charatonik, Janusz R. Prajs (2005)

Czechoslovak Mathematical Journal

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Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, λ -dendroids, dendroids, arc-like continua and arc-like λ -dendroids is an approximative...