Characterizing chainable, tree-like, and circle-like continua
نویسندگان
چکیده
منابع مشابه
Mapping Chainable Continua onto Dendroids
We prove that every chainable continuum can be mapped into a dendroid such that all point-inverses consist of at most three points. In particular, it follows that there exists a finite-to-one map from a hereditarily indecomposable continuum (the pseudoarc) onto hereditarily decomposable continuum. This answers a question by J. Krasinkiewicz.
متن کاملExactly two-to-one maps from continua onto some tree-like continua
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 ...
متن کاملThe nonexistence of expansive homeomorphisms of chainable continua
A homeomorphism f : X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x 6= y, then there is an integer n ∈ Z such that d(f(x), f(y)) > c. In this paper, we prove that if a homeomorphism f : X → X of a continuum X can be lifted to an onto map h : P → P of the pseudoarc P , then f is not expansive. As a corollary, we prove that there are no expansive ho...
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متن کاملThe fixed point property for arc component preserving mappings of non-metric tree-like continua
The main purpose of this paper is to study the fixed point property of non-metric tree-like continua. Using the inverse systems method, it is proved that if X is a non-metric tree-like continuum and if f : X → X is a mapping which sends each arc component into itself, then f has the fixed point property.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2011
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm124-1-1