On weakly bounded well-filtered spaces

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} $.

Keywords

• k-bounded well-filtered space
• weakly bounded well-filtered space
• scott topology
• smyth power space
• reflection