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A unified approach to some non-Hausdorff topological properties

Published online by Cambridge University Press:  16 March 2021

Qingguo Li,
Zhenzhu YuanOpen the ORCID record for Zhenzhu Yuan[Opens in a new window] and
Dongsheng Zhao
Qingguo Li*
Affiliation:
School of Mathematics, Hunan University, Changsha, Hunan 410082, China
Zhenzhu Yuan
Affiliation:
School of Mathematics, Hunan University, Changsha, Hunan 410082, China
Dongsheng Zhao
Affiliation:
Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, 637616, Singapore
*
*Corresponding author. Email: liqingguoli@aliyun.com
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Abstract

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Sobriety, well-filteredness, and monotone convergence are three of the most important properties of topological spaces extensively studied in domain theory. Some other weak forms of sobriety and well-filteredness have also been investigated by some authors. In this paper, we introduce the notion of Θ-fine spaces, which provides a unified approach to such properties. In addition, this general approach leads to the definitions of some new topological properties.

Keywords

Sober spaced-spaceΘ-fine spacePF-well-filtered space

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 9 , October 2020, pp. 997 - 1010
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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