.Let X,D be a metric space and Y,D|Y be a metric sub space of X( see example 4).Prove each of the following

a.A subset W of Y is open in Y,( that is,is DY-open)if and only if W=YU,where Uis an open subset of X.

b.A subset C of Y is closed in Y if and only if C=YF,where F is a closed subset of X.

Example 4: Example 4.If X is any metric space with metric D,and Y is any subset of X,then Y can also be considered to be a metric space using the same metric as X.More precisely,Y with metricD|Y (e.i D defined for pairs of elements of Y)is a metric space.Y,D|Y is said to be a subspace ofthe metric space X,D.