The answer to a problem posed by Zhao and Ho (Q1734943)

The authors present a counterexample to show that $(KB(X),\mathrm{cl})$ (where $KB(X)$ denotes the set of all irreducible closed sets of $X$ whose suprema exist) is not the canonical k-bounded sobrification of a $T_ 0$-space $X$ in the sense of \textit{K. Keimel} and \textit{J. D. Lawson} [Ann. Pure Appl. Logic 159, No. 3, 292--306 (2009; Zbl 1172.54016)] (with respect to the mapping $x\mapsto \mathrm{cl}(\{x\}))$, thus answering a question from [\textit{D. Zhao} and \textit{W. K. Ho}, J. Log. Algebr. Methods Program. 84, No. 1, 185--195 (2015; Zbl 1308.54019)]. \par They leave open the question whether the category of k-bounded sober spaces is a full reflective subcategory of the category of $T_0$-spaces.