Answer to Question #264670 in Real Analysis for Nikhil rawat

Question

Check whether the following sets are open sets

a. The set of all rational numbers.

b. Set { 1/n^2 | n∈ N}

Answer 1

a)

Q=set of all rational number

Q is not open set because every point is not interior point of Q.

b)

A=set {$\frac{1}{n^2} | n∈N$ }

If we take any neighborhood around  $\frac{1}{n^2}$

 it will not be completely contained in the set A.

This implies every interior point of A is not in A.

Therefore, A 9s not open set.