Week 10; 8.3 - 8.4 Flashcards
1
Q
Prove
A
2
Q
Prove
A
RHS if compact, LHS is not
3
Q
Prove
A
4
Q
We say that a function between metric spaces is uniformly continuous if
A
5
Q
Prove
A
6
Q
A subset K of a metric space (X,d) is said to be sequentially compact if
A
Every sequence in K has a subsequence which converted to a limit in K
7
Q
Examples of sequentially compact and not
A
8
Q
If K is sequentially compact in (X, d) and the metric ρ is equivalent to d then
A
9
Q
Prove that every closed and bounded subset of R is sequentially compact?
And note?
A
(Converse is also true)
10
Q
A metric space is totally bounded if
A
11
Q
Define a finite ε-net
A
12
Q
Prove
A
