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Displaying similar documents to “A characterization of smoothness in dendroids”

The homotopy dimension of codiscrete subsets of the 2-sphere 𝕊²

J. W. Cannon, G. R. Conner (2007)

Fundamenta Mathematicae

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Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpiński curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental...

Homotopy properties of curves

Janusz Jerzy Charatonik, Alejandro Illanes (1998)

Commentationes Mathematicae Universitatis Carolinae

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Conditions are investigated that imply noncontractibility of curves. In particular, a plane noncontractible dendroid is constructed which contains no homotopically fixed subset. A new concept of a homotopically steady subset of a space is introduced and its connections with other related concepts are studied.

Homotopy types of one-dimensional Peano continua

Katsuya Eda (2010)

Fundamenta Mathematicae

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Let X and Y be one-dimensional Peano continua. If the fundamental groups of X and Y are isomorphic, then X and Y are homotopy equivalent. Every homomorphism from the fundamental group of X to that of Y is a composition of a homomorphism induced from a continuous map and a base point change isomorphism.