## Question

###### Let (X,d) be a metric space, and let A be a subset of X_ We shall consider A with the subset metric dA- Assume that G = A is open in (X,d). Show that G is open in (A,dA): Find an example which shows that although G â‚¬ A is open in (A,dA) it need not be open in (X,dx). Show that if A is an open set in (X,dx). then a subset G of A is open in (A,dA_ if and only if it is open in (X dx)

Let (X,d) be a metric space, and let A be a subset of X_ We shall consider A with the subset metric dA- Assume that G = A is open in (X,d). Show that G is open in (A,dA): Find an example which shows that although G â‚¬ A is open in (A,dA) it need not be open in (X,dx). Show that if A is an open set in (X,dx). then a subset G of A is open in (A,dA_ if and only if it is open in (X dx)

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