In R, every nonempty open set is the disjoint union of a countable collection of open intervals. (Royden/Fitzpatrick, 4th edition)(adsbygoogle = window.adsbygoogle || []).push({});

What is the most general setting in which every open set is a disjoint union of countable collection of open balls (or bases)? In R^n? In metric spaces? In second countable topological spaces?

The above theorem in R took me by surprise when I saw it for the first time.

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# Open set is countable union of disjoint open balls

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