Summary: L. G. Huang
and X. Zhang
[J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022
)] reviewed cone metric spaces. We prove that there are no normal cones with normal constant
and for each
there are cones with normal constant
. Also, by providing non-normal cones and omitting the assumption of normality in some results of [loc. cit.], we obtain generalizations of the results.