论文标题
来自本地紧凑的可分离度量空间的不可还原商图
Irreducible Quotient Maps From Locally Compact Separable Metric Spaces
论文作者
论文摘要
令X为标准空间的Hausdorff商（这是局部紧凑的可分离度量空间）。结果表明，以下内容是等效的：（i）x是标准空间中不可还原商图的图像； （ii）X具有一个依次致密的子集，满足涉及双序列的两个技术条件； (iii) whenever q : Y\to X is a quotient map from a standard space Y , the restriction q_{\st}|V is an irreducible quotient map from V onto X (where q_{\st} : Y_{\st}\to X is the pure quotient derived from q, and V is the closure of the set of singleton fibres of Y_{\st}).该证明使用Whyburn和Zarikian从紧凑到局部紧凑的标准空间的定理的扩展。即使对于真实行的本地紧凑子集的商，结果也是新的。
Let X be a Hausdorff quotient of a standard space (that is of a locally compact separable metric space). It is shown that the following are equivalent: (i) X is the image of an irreducible quotient map from a standard space; (ii) X has a sequentially dense subset satisfying two technical conditions involving double sequences; (iii) whenever q : Y\to X is a quotient map from a standard space Y , the restriction q_{\st}|V is an irreducible quotient map from V onto X (where q_{\st} : Y_{\st}\to X is the pure quotient derived from q, and V is the closure of the set of singleton fibres of Y_{\st}). The proof uses extensions of the theorems of Whyburn and Zarikian from compact to locally compact standard spaces. The results are new even for quotients of locally compact subsets of the real line.
