The Smirnov remainders of uniformly locally connected proper metric spaces
The Smirnov remainders of uniformly locally connected proper metric spaces
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均匀局部连通的真度量空间的斯米尔诺夫余数
DOI：
10.1016/j.topol.2010.10.006
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发表时间：
2011
影响因子：
0.6
通讯作者：
Kazuo Tomoyasu
中科院分区：
文献类型：
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作者：
Yuji Akaike;Naotsugu Chinen;Kazuo Tomoyasu
本文研究了Smirnov余项的维数与一致局部连通性之间的关系。特别地，本文研究了具有一致局部连通性的n维欧氏空间（Rn，d）的Smirnov余式udRn <$Rn的维数.证明了当（R，d）局部一致连通时，dimudR <$R= indudR <$R=IndudR <$R=1.此外，我们引入了一个新的“薄”覆盖空间的概念，我们有：如果紧致2-流形的无限覆盖空间（R2，d）是“薄”的，则dimud <$R2 <$R2 =indud <$R2 <$R2 = indud <$R2 <$R2 =2。
The aim of this paper is to investigate relations between uniform local connectedness and the dimension of the Smirnov remainder. In particular, we devote this paper to calculating the dimension of the Smirnov remainder udRn∖Rnof the n-dimensional Euclidean space (Rn,d) with uniform local connectedness. We show that dimudR∖R=indudR∖R=IndudR∖R=1 if (R,d) is uniformly locally connected. Moreover, we introduce a new concept of “thin” covering spaces, and we have the following: If an infinite covering space (R2,d˜) of a compact 2-manifold is “thin”, then dimud˜R2∖R2=indud˜R2∖R2=Indud˜R2∖R2=2.