- #1
funcalys
- 30
- 1
Hi folks, as I was reviewing the metric space section in Amann- Escher textbook, I came across the following example of neighborhood:
"For [itex]\left[0,1\right][/itex] with the metric induced from [itex]R[/itex], [itex]\left[\frac{1}{2},1\right][/itex] is a neighborhood of 1, but not of [itex]\frac{1}{2}[/itex]."
However I can't point out the exactly "r">0 satisfying [itex]B_{[0,1]}(1,r)[/itex][itex]\subseteq[0,1][/itex].
"For [itex]\left[0,1\right][/itex] with the metric induced from [itex]R[/itex], [itex]\left[\frac{1}{2},1\right][/itex] is a neighborhood of 1, but not of [itex]\frac{1}{2}[/itex]."
However I can't point out the exactly "r">0 satisfying [itex]B_{[0,1]}(1,r)[/itex][itex]\subseteq[0,1][/itex].