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Mediterranean Journal of Mathematics

, Volume 10, Issue 1, pp 519–528 | Cite as

On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach

  • Katsuya Eda
  • Umed H. Karimov
  • Dušan Repovš
Article

Abstract

We construct a functor AC(−, −) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)−dimensional; and (iii) For a path connected space X, π 1(X, x) is trivial if and only if π 2(AC(X, x)) is trivial. As a corollary, AC(S 1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.

Mathematics Subject Classification (2010)

Primary 54F15 55N15 Secondary 54G20 57M05 

Keywords

Noncontractible compactum weak homotopy equivalence trivial shape Peano continuum Snake cone Alternating cone asphericity cell-like space Topologist sine curve 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Science and EngineeringWaseda UniversityTokyoJapan
  2. 2.Institute of MathematicsAcademy of Sciences of TajikistanDushanbeTajikistan
  3. 3.Faculty of Mathematics and Physics and Faculty of EducationUniversity of LjubljanaLjubljanaSlovenia

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