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A construction of noncontractible simply connected cell-like two-dimensional Peano continua

Katsuya Eda, Umed H. Karimov, Dušan Repovš (2007)

Fundamenta Mathematicae

Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...

A continuum X such that C ( X ) is not continuously homogeneous

Alejandro Illanes (2016)

Commentationes Mathematicae Universitatis Carolinae

A metric continuum X is said to be continuously homogeneous provided that for every two points p , q ∈ X there exists a continuous surjective function f : X → X such that f ( p ) = q . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum X such that the hyperspace of subcontinua of X , C ( X ) , is not continuously homogeneous.

A fixed-point anomaly in the plane

Charles L. Hagopian, Janusz R. Prajs (2005)

Fundamenta Mathematicae

We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.

A hit-and-miss topology for 2 X , Cₙ(X) and Fₙ(X)

Benjamín Espinoza, Verónica Martínez-de-la-Vega, Jorge M. Martínez-Montejano (2009)

Colloquium Mathematicae

A hit-and-miss topology ( τ H M ) is defined for the hyperspaces 2 X , Cₙ(X) and Fₙ(X) of a continuum X. We study the relationship between τ H M and the Vietoris topology and we find conditions on X for which these topologies are equivalent.

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