Dear Colleagues,
Could you please help in solving the following problem:
Let (T)\longrightarrow Y " alt="T(T)\longrightarrow Y " /> be a linear operator, where and are normed spaces. Then:
If is continuous at a single point with , then it is continuous at every point of . Here denotes the domain of .
Remark: We want to prove this proposition without using the boundedness of the operator.
Regards,
Raed.