I have 2 questions about precompactness in sequence spacesDoh)
1. Is A = { } is precompact in = set of all sequences converging to 0 equipped with the sup norm ?
2. Is A= { as } in ?
1. We notice that if we have . Given an , we can find a such that . We can conclude because is precompact.
2. Let the sequence defined by .
We notice that and if . We conclude that is not precompact.