An additivity theorem for uniformly continuous functions
An additivity theorem for uniformly continuous functions
复制标题
一致连续函数的可加性定理
DOI：
10.1016/j.topol.2003.05.007
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
J. Pelant
中科院分区：
文献类型：
--
作者：
A. Berarducci;D. Dikranjan;J. Pelant
我们考虑度量空间X具有一个很好的性质，即任何连续函数f：X→ R在X的有限闭集覆盖的每一个集合上一致连续，它本身也是一致连续的。我们在所有局部连通度量空间的充分类中刻画了具有这一性质的空间。事实证明，它们与一致局部连通空间一致，因此它们包括，例如，所有拓扑向量空间。另一方面，在所有完全不连通空间的类中，这些空间与UC空间重合。
We consider metric spaces X with the nice property that any continuous function f :X→ R which is uniformly continuous on each set of a finite cover of X by closed sets, is itself uniformly continuous. We characterize the spaces with this property within the ample class of all locally connected metric spaces. It turns out that they coincide with the uniformly locally connected spaces, so they include, for instance, all topological vector spaces. On the other hand, in the class of all totally disconnected spaces, these spaces coincide with the UC spaces.