I apologyze for my notation.
I will copy once again the problem, using a better notation.
Let X and Y be non empty sets. X is a compact set and Y is a closed set. Show that ∃ α∈X and β∈Y such that |α-β|≤|x-y| ∀ x∈X and ∀ y∈Y
I need help with this problem:
Let X and Y be sets that are non empty and are different. Where X is compact and Y is a closed set.
Show that there exist x_{o} in X and y_{o} in Y such that |x_{o}-y_{o}|<= |x-y| for all x in X and y in Y.
Thanks
I apologyze for my notation.
I will copy once again the problem, using a better notation.
Let X and Y be non empty sets. X is a compact set and Y is a closed set. Show that ∃ α∈X and β∈Y such that |α-β|≤|x-y| ∀ x∈X and ∀ y∈Y