# Math Help - subsets problem in metric spaces

1. ## subsets problem in metric spaces

let X be a metric space and A an open subset of X
Prove that A ∩ B ⊂ (A∩B)

My approach:
let x∈A ∩ B
Then x∈A and x∈B
nbhd(x) intersects A and B for all ε >0
so x∈ AB
but (A∩B)AB
Did I do anything wrong or miss something?

2. ## Re: subsets problem in metric spaces

**I was Wrong