If we take X=R and Y=Z and E=N i.e. {1,2,3,4,5.........} then since for this case E is open in Y (as Y is itself an entire metric space) however there does not exist any open set G in X for this particular set. then how E is open in Y.
Pl clarify
If we take X=R and Y=Z and E=N i.e. {1,2,3,4,5.........} then since for this case E is open in Y (as Y is itself an entire metric space) however there does not exist any open set G in X for this particular set. then how E is open in Y.
Pl clarify