On almost sober spaces

作者：Shan, Qidong; Bao, Meng; Wen, Xinpeng; Xu, Xiaoquan^*

来源：TOPOLOGY AND ITS APPLICATIONS, 2022, 305: 107896.

DOI：10.1016/j.topol.2021.107896

• Almost sober space
• Hereditary property
• Retract
• Function space
• Smyth power space
• Reflection

In this paper, we mainly investigate some basic properties of almost sober spaces. For the category ASob of all almost sober spaces with continuous mappings, it is proved that the ASob-reflection of Johnstone space Sigma J does not exist and hence ASob is not reflective in the category Top(0) of all T-0 spaces with continuous mappings. It is shown that some properties which are similar to that of sober spaces hold and others do not hold.

• 单位
  四川大学; 南昌航空大学