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## Main Question or Discussion Point

I almost every single case that I've seen the distance function is identical to the metric. However there are two important exceptions which are found in Schut'z

Other texts use the term "distance function" and "metric" to mean the same thing. Has anyone every heard of this or seen this in those texts? Has anyone seen it as a problem in any case either for or against the distance function being the same as the metric or not being the same as the metric?

Thank you

Pete

*Geometrical methods of mathematical physics*and in Walds*General Relativity*. Schutz refers to a "distance function" between two points on page 1 and as one exampe this function is the usual Euclidean distance function, and other examples are similar. In Wald he speaks of an open ball in R^{n}in which the Euclidean function is used as the "open ball" function about a particular point. The purpose of the distance function is to defined open and closed sets. The metric doesn't neccesarily have this ability.Other texts use the term "distance function" and "metric" to mean the same thing. Has anyone every heard of this or seen this in those texts? Has anyone seen it as a problem in any case either for or against the distance function being the same as the metric or not being the same as the metric?

Thank you

Pete