Week 6; 6.1 And 6.2 Flashcards
1
Q
Define a Cauchy sequence in a metric space
A
2
Q
Prove cauchy’s convergence criterion on a metric space
A
3
Q
Prove that if a Cauchy sequence has a convergent subsequence, that they are convergent to they same limit
A
4
Q
Define a complete metric space
A
5
Q
Give example of complete and incomplete metric spaces
A
6
Q
Prove the subspace (A, d) for A€X and (X, d) complete subspace is also complete
A
7
Q
Define the completion of an arbitrary metric space (X, d)
A
8
Q
Define the completion of (A,d) a subspace of the complete metric space (X,d)
A
9
Q
Prove that B(s) is complete with the uniform metric
A
10
Q
Prove that C[a,b] is complete with the uniform metric
A
