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## Main Question or Discussion Point

So I'm trying to teach myself some topology, and the first thing I noticed, was that a metric space is a topological space under the topology of all open balls..

But then, consider the intersection of two open balls, can someone prove to me that the result is another open ball?

Or do they mean, that the topology is the set of all open balls, finite intersections of open balls, and arbitrary unions of open balls?

edit: How do I use latex notation on these forums?

But then, consider the intersection of two open balls, can someone prove to me that the result is another open ball?

Or do they mean, that the topology is the set of all open balls, finite intersections of open balls, and arbitrary unions of open balls?

edit: How do I use latex notation on these forums?