The stupid question of the day.(adsbygoogle = window.adsbygoogle || []).push({});

If S is the real interval (-infinite, 5], and I can find a metric d so that (S,d) is a metric space, then,

is, for example, (4, 5] an open set in (S,d) ?

I say this because, the way I'm reading the definition of an open ball, the open ball B(5,1) is the interval (4,5] and not the interval (4,6), since the points in (5,6) do not belong to the metric space (S,d). So every open ball in (4,5] centered in 5 is completely contained in (4,5].

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# Question about open sets in (-infinite,5]

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