# Question about open sets in [0,1]

1. Apr 10, 2010

### AxiomOfChoice

Isn't [0,1) open in [0,1]? I know it's not open in $\mathbb R$, but I sincerely hope it's open in [0,1].

2. Apr 10, 2010

### Hurkyl

Staff Emeritus
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).