Recently, Du (J Nonlinear Anal 72:2259-2261, 2010) by using a nonlinear scalarization function, in the setting of locally convex topological vector spaces, could transfer a cone metric space to a usual metric space. Simultaneously, Amini-Harandi and Fakhar (Com Math Appl 59:3529-3534, 2010) by using a notion of base for the cone, in the setting of Banach spaces, could do the same. In this note we will see that two methods coincide and moreover they are valid for topological vector spaces and it is not necessary that we only consider the cones which have a compact base. Finally, it is worth noting that the nature of this note is similar to Caglar and Ercan (Order-unit-metric spaces, arXiv:1305.6070 [math.FA], 2013).
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机译：最近，Du（J Nonlinear Anal 72：2259-2261，2010）通过使用非线性标量函数，在局部凸拓扑向量空间的设置中，可以将圆锥度量空间转换为常规度量空间。同时，Amini-Harandi和Fakhar（Com Math Appl 59：3529-3534，2010）通过在Banach空间的设置中使用锥底的概念可以做到这一点。在本说明中，我们将看到两种方法是重合的，而且它们对于拓扑向量空间都是有效的，并且没有必要只考虑具有紧凑底数的圆锥体。最后，值得注意的是，本注释的性质类似于Caglar和Ercan（Order-unit-metric space，arXiv：1305.6070 [math.FA]，2013年）。
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