  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
$X$, $\pi_1(X,x)$ is trivial if and only if $\pi_2(AC(X, x))$ is trivial. As a
corollary, $AC(S^1, x)$ is a 2-dimensional nonaspherical cell-like Peano
continuum.
