Why is it necessary for one of the sets in the Minkowski sum to be bounded (given that both sets are closed) in order that the Minkowski sum be closed?
[Edit: In view of @robjohn 's comment (thanks!), I should perhaps change the question to: "Why is it necessary for one of the sets in the Minkowski sum to be bounded (given that both sets are closed) in order to guarantee that the Minkowski sum be closed?]
Also, what are the conditions for the Minkowski sum to be open?
Thanks.