二维非球面胞状Peano连续统的一种简化方法
On 2-dimensional nonaspherical cell-like Peano continua: A simplified approach
摘要：
我们构造了一个从具有基点$x$的路连通空间范畴$X$到单连通空间范畴的函子$AC(-,-)$.本文的主要结果如下：（i）若$X$是Peano连续统，则$AC(X,x)$是胞状Peano连续统;（ii）若$X$是$n-$维，则$AC(X, x)$是$(n+1)-$维;（iii）对于路径连通空间$X$，$π_1(X,x)$平凡当且仅当$π_2(AC(X, x))$平凡.作为推论，$AC(S^1, x)$是一个二维非球面胞状Peano连续体。
英文摘要：
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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