1. The Answer to a Problem Posed by Zhao and Ho.
- Author
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Zhao, Bin, Lu, Jing, and Wang, Kai Yun
- Subjects
K-spaces ,SET theory ,K-theory ,TOPOLOGICAL spaces ,MATHEMATICS - Abstract
Zhao and Ho asked in a recent paper that for each T
0 space X, whether KB(X) (the set of all irreducible closed sets of X whose suprema exist) is the canonical k-bounded sobrification of X in the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategory Topκ of the category Top0 of T0 spaces, and prove that the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category Topκ . [ABSTRACT FROM AUTHOR]- Published
- 2019
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