Consider the linear map . Then . To conclude, show that is linear and bounded.
Please explain more
What don't you understand exactly?
I want to prove that a group be closed
What do you mean? Where do you see a group?
Are you sure this course work is from a class you are taking? You seem to be saying that you do not know what any of this means. For example, do you know what " " means? How is the topology defined on that set ("group" is, mathematically, the wrong word)? How is "closed" defined in that topology?