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. Thefollowing are the main results of the paper: (i) If $X$ is a Peano continuumthen $AC(X,x)$ is a cell-like Peano continuum; (ii) If $X$ is $n-$dimensionalthen $AC(X, x)$ is $(n+1)-$dimensional; and (iii) For a path connected space$X$, $\pi_1(X,x)$ is trivial if and only if $\pi_2(AC(X, x))$ is trivial. As acorollary, $AC(S^1, x)$ is a 2-dimensional nonaspherical cell-like Peanocontinuum.
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机译：我们从路径连通的空间$ X $的类别构造一个函子$ AC（-，-）$，其基点$ x $指向简单连通的空间的类别。以下是本文的主要结果：（i）如果$ X $是Peano连续体，则$ AC（X，x）$是像细胞的Peano连续体； （ii）如果$ X $是$ n-维，则$ AC（X，x）$是$（n + 1）-维； （iii）对于路径连接的空间$ X $，当且仅当$ \ pi_2（AC（X，x））$不重要时，$ \ pi_1（X，x）$是不重要的。作为推论，$ AC（S ^ 1，x）$是二维非球面细胞样Peanocontinuum。
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