Originally Posted by

**math_help** Need help proving the following statements/giving counter-examples;

(X,d) is a metric space

1: for all a єX, U n=1 --> ∞, B(1/n, a) is an open set

2: for all a єX, U n=1 --> ∞, B(1/n, a) is not an open set

3: if xn --> x, then any subsequence of xn converges to x

4: if any subsequence of xn converges to x, then xn converges to x

5: if U is open then U=Int(Uconjugate)

So I guess, 1 is true, 2 false, 3 true, 4 false, 5 no idea

I'm generally stuck with it all, my idea for 1 is that in general you can always choose an ε greater than the radius of 1/n so it is open...is this right?