### 10 Let ( X ) be a normed space and ( f: X rightarrow mathbf{K} ) be linear. Then ( f ) is closed if and only if ( f ) is continuous. (Hint: ( 6.4 ) and Problem 10-2) 10f4 Let ( X ) be an infinite dimensional normed space. If ( Y ) is a nonzero normed space, then there is some ( F: X rightarrow Y ) which is linear but not closed. 125

10 Let ( X ) be a normed space and ( f: X rightarrow mathbf{K} ) be linear. Then ( f ) is closed if and only if ( f ) is continuous. (Hint: ( 6.4 ) and Problem 10-2) 10f4 Let ( X ) be an infinite dimensional normed space. If ( Y ) is a nonzero normed space, then there is some ( F: X rightarrow Y ) which is linear but not closed. 125