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.
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Eda, K., Karimov, U.H. & Repovš, D. On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach. Mediterr. J. Math. 10, 519–528 (2013). https://doi.org/10.1007/s00009-011-0165-1
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DOI: https://doi.org/10.1007/s00009-011-0165-1