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On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach |
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| Authors: | Katsuya Eda Umed H Karimov Du?an Repov? |
| Institution: | 1. School of Science and Engineering, Waseda University, 169-8555, Tokyo, Japan 2. Institute of Mathematics, Academy of Sciences of Tajikistan, Ul. Ainy 299A, 734063, Dushanbe, Tajikistan 3. Faculty of Mathematics and Physics and Faculty of Education, University of Ljubljana, P. O. Box 2964, 1001, Ljubljana, Slovenia |
| 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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