Talk:Metric space

Zundark: For people like me who know almost nothing about it, why did you change the definition as you just did? Is your definition correct and the prior one incorrect, or are the two equivalent, with you just preferring one over the other? If so, why are they equivalent? Thanks, SJK.

They are equivalent, since the open ball is defined to be a subset of the metric space. LC changed the definition yesterday for some reason. I left it alone at the time, but this morning I decided I prefer the original definition, so I changed it back. I just feel that using "subset" could be a bit misleading, considering that it cannot be a proper subset. --Zundark, 2001 Dec 30

While not as elegant, maybe it is easier to understand if we first define a subset of a metric space to be bounded if it is subset of a ball, and then define the whole space to be bounded if it is bounded as a subset of itself. (Boundedness of the whole space is IMHO not as commonly encountered as boundedness of subsets.) --AxelBoldt

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I just removed the following:

Applications in science cosmology - the FLRW metric. The metric of the spacetime of the universe, according to the standard big bang model, which as of 2002 was required by and consistent with all experiments and observations of spacetime events both close and as far away as possible from the spacetime event called human civilisation, is generally called the FLRW metric, and can be written in a spherically symmetric form such as:

• ds² = -c²dt² + a² ( dr² /(1 - k r²)) + r² (dθ² + sin²θ dφ²) )

This should go into an article about pseudo Riemannian manifolds somewhere. It is not related to the mathematical concept of metric space. AxelBoldt 11:40 Aug 28, 2002 (PDT)