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Apr 19, 2016 at 4:12 comment added Nate Eldredge Perhaps it should be made clear that the algebra you mention needs to contain all the open sets. Certainly the indicator of an open set (or at least an open ball) can be written as a pointwise limit of continuous functions, but we are taking advantage of the metric here.
May 22, 2014 at 18:24 vote accept TV2323
May 22, 2014 at 0:51 history answered Alexander Shamov CC BY-SA 3.0