Existence of well-filterifications of T₀ topological spaces
We prove that for every T0 space X, there is a well-filtered space W(X) and a continuous mapping ηX:X⟶W(X), such that for any well-filtered space Y and any continuous mapping f:X⟶Y there is a unique continuous mapping fˆ:W(X)⟶Y such that f=fˆ∘ηX. Such a space W(X) will be called the well-filterifica...
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sg-ntu-dr.10356-1548912022-01-13T03:35:37Z Existence of well-filterifications of T₀ topological spaces Wu, Guohua Xi, Xiaoyong Xu, Xiaoquan Zhao, Dongsheng School of Physical and Mathematical Sciences Science::Mathematics Directed Complete Poset Scott Topology We prove that for every T0 space X, there is a well-filtered space W(X) and a continuous mapping ηX:X⟶W(X), such that for any well-filtered space Y and any continuous mapping f:X⟶Y there is a unique continuous mapping fˆ:W(X)⟶Y such that f=fˆ∘ηX. 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. Ministry of Education (MOE) Nanyang Technological University This work was supported by Ministry of Education - Singapore Academic Research Fund Tier 2 grant MOE2016-T2-1-083 (M4020333); NTU Tier 1 grants RG32/16 (M4011672); NSFC (11661057); the Ganpo 555 project for leading talent of Jiangxi Province and the Natural Science Foundation of Jiangxi Province, China (20161BAB2061004); NSFC (11361028, 61300153, 11671008, 11701500, 11626207); NSF Project of Jiangsu Province, China (BK20170483); NIE AcRF (RI 3/16 ZDS), Singapore. 2022-01-13T03:35:37Z 2022-01-13T03:35:37Z 2020 Journal Article Wu, G., Xi, X., Xu, X. & Zhao, D. (2020). Existence of well-filterifications of T₀ topological spaces. Topology and Its Applications, 270, 107044-. https://dx.doi.org/10.1016/j.topol.2019.107044 0166-8641 https://hdl.handle.net/10356/154891 10.1016/j.topol.2019.107044 2-s2.0-85076922880 270 107044 en MOE2016-T2-1-083 (M4020333) RG32/16 (M4011672) RI 3/16 ZDS Topology and its Applications © 2019 Elsevier B.V. All rights reserved. |
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Science::Mathematics Directed Complete Poset Scott Topology Wu, Guohua Xi, Xiaoyong Xu, Xiaoquan Zhao, Dongsheng Existence of well-filterifications of T₀ topological spaces |
| description |
We prove that for every T0 space X, there is a well-filtered space W(X) and a continuous mapping ηX:X⟶W(X), such that for any well-filtered space Y and any continuous mapping f:X⟶Y there is a unique continuous mapping fˆ:W(X)⟶Y such that f=fˆ∘ηX. 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. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Wu, Guohua Xi, Xiaoyong Xu, Xiaoquan Zhao, Dongsheng |
| format |
Article |
| author |
Wu, Guohua Xi, Xiaoyong Xu, Xiaoquan Zhao, Dongsheng |
| author_sort |
Wu, Guohua |
| title |
Existence of well-filterifications of T₀ topological spaces |
| title_short |
Existence of well-filterifications of T₀ topological spaces |
| title_full |
Existence of well-filterifications of T₀ topological spaces |
| title_fullStr |
Existence of well-filterifications of T₀ topological spaces |
| title_full_unstemmed |
Existence of well-filterifications of T₀ topological spaces |
| title_sort |
existence of well-filterifications of t₀ topological spaces |
| publishDate |
2022 |
| url |
https://hdl.handle.net/10356/154891 |
| _version_ |
1722355358835408896 |