Existence of well-filterifications of T₀ topological spaces

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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Bibliographic Details
Main Authors: Wu, Guohua, Xi, Xiaoyong, Xu, Xiaoquan, Zhao, Dongsheng
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
Subjects:
Science::Mathematics
Directed Complete Poset
Scott Topology
Online Access:https://hdl.handle.net/10356/154891
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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