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.