On T0 spaces determined by well-filtered spaces

Xu, Xiaoquan; Shen, Chong; Xi, Xiaoyong; Zhao, Dongsheng

doi:10.1016/j.topol.2020.107323

Cited by 35 publications

(69 citation statements)

References 14 publications

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“…It is well-known that every sober space is well-filtered (see [28]) and every well-filtered space is a d-space (cf. [47,51]). The Scott space of every continuous dcpo is sober (see [19]).…”

Section: Well-filtered Spaces and Sober Spacesmentioning

confidence: 99%

“…This problem was first solved by Lawson and Xi [35], and later answered by Xu, Shen, Xi and Zhao [51,52] using a different method.…”

Section: Theorem 34 ([53]mentioning

confidence: 99%

“…It is easy to verify that closed subspaces, retracts and products of DC spaces are again DC spaces (see [51]).…”

Section: Rudin Sets and Well-filtered Determined Setsmentioning

confidence: 99%

“…Based on the topological Rudin's Lemma, we introduce a new type of spaces -Rudin spaces (see [42,51]).…”

Section: Rudin Sets and Well-filtered Determined Setsmentioning

confidence: 99%

“…The sets in WD(X) are called WD sets. The space X is called a well-filtered determined space, shortly a WD space, if all irreducible closed subsets of X are WD sets, that is, Irr c (X) = WD(X) (see [49,51]).…”

Section: Rudin Sets and Well-filtered Determined Setsmentioning

confidence: 99%

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Some open problems on well-filtered spaces and sober spaces

Zhao

2021

Topology and its Applications

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“…It is well-known that every sober space is well-filtered (see [28]) and every well-filtered space is a d-space (cf. [47,51]). The Scott space of every continuous dcpo is sober (see [19]).…”

Section: Well-filtered Spaces and Sober Spacesmentioning

confidence: 99%

“…This problem was first solved by Lawson and Xi [35], and later answered by Xu, Shen, Xi and Zhao [51,52] using a different method.…”

Section: Theorem 34 ([53]mentioning

confidence: 99%

“…It is easy to verify that closed subspaces, retracts and products of DC spaces are again DC spaces (see [51]).…”

Section: Rudin Sets and Well-filtered Determined Setsmentioning

confidence: 99%

“…Based on the topological Rudin's Lemma, we introduce a new type of spaces -Rudin spaces (see [42,51]).…”

Section: Rudin Sets and Well-filtered Determined Setsmentioning

confidence: 99%

Section: Rudin Sets and Well-filtered Determined Setsmentioning

confidence: 99%

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Some open problems on well-filtered spaces and sober spaces

Zhao

2021

Topology and its Applications

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On Some Topological Properties of Dcpo Models of $$T_1$$ Topological Spaces

Chen

2022

Results Math

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A direct approach to K-reflections of T0 spaces

2020

Topology and its Applications

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In this paper, we provide a direct approach to K-reflections of T 0 spaces. For a full subcategory K of the category of all T 0 spaces and a T 0 space X, let K(X) = {A ⊆ X : A is closed and for any continuousWe call K an adequate category if for any T 0 space X, P H (K(X)) is a K-space. Therefore, if K is adequate, then K is reflective in Top 0 . It is shown that the category of all sober spaces, that of all d-spaces, that of all well-filtered spaces and the Keimel and Lawson's category are all adequate, and hence are all reflective in Top 0 . Some major properties of K-spaces and K-reflections of T 0 spaces are investigated. In particular, it is proved that if K is adequate, then the K-reflection preserves finite products of T 0 spaces. Our study also leads to a number of problems, whose answering will deepen our understanding of the related spaces and their categorical structures.

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On T0 spaces determined by well-filtered spaces

Cited by 35 publications

References 14 publications

Some open problems on well-filtered spaces and sober spaces

Some open problems on well-filtered spaces and sober spaces

On Some Topological Properties of Dcpo Models of $$T_1$$ Topological Spaces

A direct approach to K-reflections of T0 spaces

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