论文标题

使空间野外(简单地连接的情况)

Making spaces wild (simply-connected case)

论文作者

Eda, Katsuya

论文摘要

我们将圆的副本附加到可分离的度量空间的可数密度子集$ d $ $ x $和 构建耳环空间$ e(x,d)$。我们表明,如果Space $ X $简单地连接并且本地与之相关,则$ E(x,d)$的基本组对夏威夷耳环组的子组是同构的。此外,如果$ x $是本地路径连接的,则可以从$ e(x,d)$的基本组中回收空间$ x $。

We attach copies of the circle to points of a countable dense subset $D$ of a separable metric space $X$ and construct an earring space $E(X,D)$. We show that the fundamental group of $E(X,D)$ is isomorphic to a subgroup of the Hawaiian earring group, if the space $X$ is simply-connected and locally simply-connected. In addition if the space $X$ is locally path-connected, the space $X$ can be recovered from the fundamental group of $E(X,D)$.

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