If are two distinct points in a metric space then there exists such that and are disjoint. So let . Choose . Then and are disjoint for all ? Is this right? e.g. where ?

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Originally Posted by particlejohn If are two distinct points in a metric space then there exists such that and are disjoint. So let . Choose . Then and are disjoint for all ? If they're open balls, yep. Is this right? e.g. where ? Isn't there a problem with the indices?

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