Sequence-covering maps of metric spaces
Sequence-covering maps of metric spaces
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DOI：
10.1016/s0166-8641(99)00163-7
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发表时间：
2001-02
影响因子：
0.6
通讯作者：
Shou Lin;P. Yan
中科院分区：
文献类型：
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作者：
Shou Lin;P. Yan
设f：X，→，Y是一个映射。F是一个序列覆盖映射，如果当{Yn}是Y中的收敛序列时，X中有一个收敛序列{xn}，每个xn∈f−1(Yn)。F是1序列覆盖映射，如果对每个y∈Y，都有x∈f−1(Y)使得只要{yn}是收敛到y的序列，就有一个序列{xn}收敛到X中的x，其中每个xn∈f−1(Yn).本文研究了度量空间的序列覆盖像的结构，主要结果是
Let f :X→Y be a map. f is a sequence-covering map if whenever {yn} is a convergent sequence in Y , there is a convergent sequence {xn} in X with each xn∈f−1(yn) . f is a 1-sequence-covering map if for each y∈Y , there is x∈f−1(y) such that whenever {yn} is a sequence converging to y in Y there is a sequence {xn} converging to x in X with each xn∈f−1(yn) . In this paper we investigate the structure of sequence-covering images of metric spaces, the main results are that