On weakly bounded well-filtered spaces

Xiaoyuan Zhang; Meng Bao; Xinpeng Wen; Xiaoquan Xu; Xiaoyuan Zhang; Meng Bao; Xinpeng Wen; Xiaoquan Xu

doi:10.3934/math.2022936

AIMS Mathematics

2022, Volume 7, Issue 9: 17026-17044. doi: 10.3934/math.2022936

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Research article

On weakly bounded well-filtered spaces

1.
School of Big Data Science, Hebei Finance University, Baoding 071051, China
2.
College of Mathematics, Sichuan University, Chengdu 610064, China
3.
College of Mathematics and Information, Nanchang Hangkong University, Nanchang 330063, China
4.
Fujian Key Laboratory of Granular Computing and Applications, Minnan Normal University, Zhangzhou 363000, China

Received: 31 March 2022 Revised: 05 June 2022 Accepted: 12 June 2022 Published: 19 July 2022
MSC : 06B35, 06F30, 18B30, 54D35

In ^[16], using Rudin sets, Miao, Li and Zhao introduced a new concept of weakly well-filtered spaces—$ k $-bounded well-filtered spaces. Now, also using Rudin sets, we introduce another type of $ T_0 $ spaces—weakly bounded well-filtered spaces, which are strictly stronger than $ k $-bounded well-filtered spaces. Some basic properties of $ k $-bounded well-filtered spaces and weakly bounded well-filtered spaces are investigated and the relationships among some kinds of weakly sober spaces and weakly well-filtered spaces are posed. It is proved that the category $ {\bf KBWF} $ is not reflective in the category $ {\bf Top}_{0} $.
- $ k $-bounded well-filtered space,
- weakly bounded well-filtered space,
- Scott topology,
- Smyth power space,
- reflection
Citation: Xiaoyuan Zhang, Meng Bao, Xinpeng Wen, Xiaoquan Xu. On weakly bounded well-filtered spaces[J]. AIMS Mathematics, 2022, 7(9): 17026-17044. doi: 10.3934/math.2022936

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Abstract

In ^[16], using Rudin sets, Miao, Li and Zhao introduced a new concept of weakly well-filtered spaces—$ k $-bounded well-filtered spaces. Now, also using Rudin sets, we introduce another type of $ T_0 $ spaces—weakly bounded well-filtered spaces, which are strictly stronger than $ k $-bounded well-filtered spaces. Some basic properties of $ k $-bounded well-filtered spaces and weakly bounded well-filtered spaces are investigated and the relationships among some kinds of weakly sober spaces and weakly well-filtered spaces are posed. It is proved that the category $ {\bf KBWF} $ is not reflective in the category $ {\bf Top}_{0} $.

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