Displaying similar documents to “On the continua which are Cantor homogeneous or arcwise homogeneous”

Continuous mappings on continua II

T. Maćkowiak, E. D. Tymchatyn

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CONTENTSIntroduction......................................................................................51. General notion of aposyndesis....................................................62. Relation T for special families......................................................83. Properties of T.............................................................................94. T-aposyndesis in homogeneous continua..................................115. Colocal connectedness and T-aposyndesis...............................136....

1/2-Homogeneous hyperspace suspensions

Sergio Macías, Patricia Pellicer-Covarrubias (2012)

Colloquium Mathematicae

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We continue the study of 1/2-homogeneity of the hyperspace suspension of continua. We prove that if X is a decomposable continuum and its hyperspace suspension is 1/2-homogeneous, then X must be continuum chainable. We also characterize 1/2-homogeneity of the hyperspace suspension for several classes of continua, including: continua containing a free arc, atriodic and decomposable continua, and decomposable irreducible continua about a finite set.

Absolute n-fold hyperspace suspensions

Sergio Macías, Sam B. Nadler, Jr. (2006)

Colloquium Mathematicae

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The notion of an absolute n-fold hyperspace suspension is introduced. It is proved that these hyperspaces are unicoherent Peano continua and are dimensionally homogeneous. It is shown that the 2-sphere is the only finite-dimensional absolute 1-fold hyperspace suspension. Furthermore, it is shown that there are only two possible finite-dimensional absolute n-fold hyperspace suspensions for each n ≥ 3 and none when n = 2. Finally, it is shown that infinite-dimensional absolute n-fold hyperspace...

A weakly chainable uniquely arcwise connected continuum without the fixed point property

Mirosław Sobolewski (2015)

Fundamenta Mathematicae

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A continuum is a metric compact connected space. A continuum is chainable if it is an inverse limit of arcs. A continuum is weakly chainable if it is a continuous image of a chainable continuum. A space X is uniquely arcwise connected if any two points in X are the endpoints of a unique arc in X. D. P. Bellamy asked whether if X is a weakly chainable uniquely arcwise connected continuum then every mapping f: X → X has a fixed point. We give a counterexample.

No arc-connected treelike continuum is the 2-to-1 image of a continuum

Jo Heath, Van C. Nall (2003)

Fundamenta Mathematicae

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In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. In 2003 we show that no arc-connected treelike continuum is the 2-to-1 image of a continuum.

Whitney properties

J. Krasinkiewicz, Sam Nadler (1978)

Fundamenta Mathematicae

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