Question about open sets in [0,1]

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SUMMARY

The set [0,1) is indeed an open set in the topological space [0,1]. While [0,1) is not open in the standard topology of the real numbers \mathbb{R}, it qualifies as open when considered within the subspace topology of [0,1]. The proof involves identifying an open set in \mathbb{R} that intersects with [0,1] to yield [0,1). This confirms the validity of [0,1) being open in the context of [0,1].

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AxiomOfChoice
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Isn't [0,1) open in [0,1]? I know it's not open in [itex]\mathbb R[/itex], but I sincerely hope it's open in [0,1].
 
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Yes, it is. The easiest way to prove it is probably to find an open set in R whose intersection with [0,1] is [0,1).
 

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