Existence of well-filterifications of T₀ topological spaces

• 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
• Institution: Nanyang Technological University

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...