Displaying similar documents to “Characterizing chainable, tree-like, and circle-like continua”

Non-additivity of the fixed point property for tree-like continua

C. L. Hagopian, M. M. Marsh (2015)

Fundamenta Mathematicae

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We investigate the fixed point property for tree-like continua that are unions of tree-like continua. We obtain a positive result if finitely many tree-like continua with the fixed point property have dendrites for pairwise intersections. Using Bellamy's seminal example, we define (i) a countable wedge X̂ of tree-like continua, each having the fpp, and X̂ admitting a fixed-point-free homeomorphism, and (ii) two tree-like continua H and K such that H, K, and H∩ K have the fixed point...

Exactly two-to-one maps from continua onto some tree-like continua

Wojciech Dębski, J. Heath, J. Mioduszewski (1992)

Fundamenta Mathematicae

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It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua and Ingram continua. The conjecture that all tree-like continua have this property, stated...

Arc property of Kelley and absolute retracts for hereditarily unicoherent continua

Janusz J. Charatonik, Włodzimierz J. Charatonik, Janusz R. Prajs (2003)

Colloquium Mathematicae

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We investigate absolute retracts for hereditarily unicoherent continua, and also the continua that have the arc property of Kelley (i.e., the continua that satisfy both the property of Kelley and the arc approximation property). Among other results we prove that each absolute retract for hereditarily unicoherent continua (for tree-like continua, for λ-dendroids, for dendroids) has the arc property of Kelley.