### 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 |

### Fingerprint

### 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)

### Cite this

*Mediterranean Journal of Mathematics*,

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

**On 2-dimensional Nonaspherical Cell-like Peano Continua : A Simplified Approach.** / Eda, Katsuya; Karimov, Umed H.; Repovš, Dušan.

Research output: Contribution to journal › Article

*Mediterranean Journal of Mathematics*, vol. 10, no. 1, pp. 519-528. https://doi.org/10.1007/s00009-011-0165-1

}

TY - JOUR

T1 - On 2-dimensional Nonaspherical Cell-like Peano Continua

T2 - A Simplified Approach

AU - Eda, Katsuya

AU - Karimov, Umed H.

AU - Repovš, Dušan

PY - 2013/2

Y1 - 2013/2

N2 - 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, π1(X, x) is trivial if and only if π2(AC(X, x)) is trivial. As a corollary, AC(S1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.

AB - 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, π1(X, x) is trivial if and only if π2(AC(X, x)) is trivial. As a corollary, AC(S1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.

KW - Alternating cone

KW - asphericity

KW - cell-like space

KW - Noncontractible compactum

KW - Peano continuum

KW - Snake cone

KW - Topologist sine curve

KW - trivial shape

KW - weak homotopy equivalence

UR - http://www.scopus.com/inward/record.url?scp=84873993598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873993598&partnerID=8YFLogxK

U2 - 10.1007/s00009-011-0165-1

DO - 10.1007/s00009-011-0165-1

M3 - Article

AN - SCOPUS:84873993598

VL - 10

SP - 519

EP - 528

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

IS - 1

ER -