Talk:Metric spaces

I can't understand this:


 * A subset X of M is open if for every point x of X there is a strictly positive number r such that B (x ; r) is contained in X. With this definition, every metric space is automatically a topological space.

What does B (x ; r) saying?

Is it saying that the set of all open balls of the metric space is a topology for the metric space? -- Simon J Kissane

No. I've rewritten the explanation. Do you understand it now?

Zundark, 2001-08-11

While the new definition is certainly correct, maybe we should point out that the union can (and usually is)

a union of infinitely many sets balls.

Also, maybe the example Rn with euclidean metric could be given. --AxelBoldt

Would it be possible to move this page to metric space (no s)?


 * Yes, it needs to be changed. I would have done it already, except that it really requires changing all the links to it (links to redirected pages being somewhat undesirable for a number of reasons). --Zundark, 2001 Sep 24