Existence of well-filterifications of T0 topological spaces

被引:11
作者
Wu, Guohua [1 ]
Xi, Xiaoyong [1 ]
Xu, Xiaoquan [2 ]
Zhao, Dongsheng [3 ]
机构
[1] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore, Singapore
[2] Minnan Normal Univ, Sch Math & Stat, Zhangzhou 363000, Fujian, Peoples R China
[3] Nanyang Technol Univ, Natl Inst Educ, Math & Math Educ, Singapore, Singapore
关键词
Directed complete poset; Scott topology; Sober space; Well-filtered space; FILTERED SPACES;
D O I
10.1016/j.topol.2019.107044
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove that for every T-0 space X, there is a well-filtered space W(X) and a continuous mapping eta(X) : X -> W(X), such that for any well-filtered space Y and any continuous mapping t: X -> Y there is a unique continuous mapping (f) over cap : W(X) -> Y such that f = (f) over cap o eta(X). Such a space W(X) will be called the well-filterification of X. This result gives a positive answer to one of the major open problems on well-filtered spaces. As a corollary, we obtain that the product of well-filtered spaces is well-filtered. (C) 2019 Elsevier B.V. All rights reserved.
引用
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页数:8
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