### 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.

Original language | English |
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Pages (from-to) | 519-528 |

Number of pages | 10 |

Journal | Mediterranean Journal of Mathematics |

Volume | 10 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Feb |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Eda, K., Karimov, U. H., & Repovš, D. (2013). On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach.

*Mediterranean Journal of Mathematics*,*10*(1), 519-528. https://doi.org/10.1007/s00009-011-0165-1