week 2 Flashcards
1
Q
Open ball
A
2
Q
Closed ball?
A
3
Q
With usual metric, denote
A
4
Q
With usual metric what form
A
5
Q
A
6
Q
Definition from balls
A
That is, U is neighbourhood of there is a ball of x in U
7
Q
Define an open set U in (X, d)
A
8
Q
A
9
Q
A
10
Q
And significance?
A
11
Q
A
12
Q
A
13
Q
A
14
Q
A
15
Q
A
16
Q
A
17
Q
A
18
Q
For an equivalent metric?
A
19
Q
x€A is said to be an interior point of A if
A
There exists an open ball lying in A
20
Q
The interior of set A is
A
21
Q
A
22
Q
If a set coincides with the union of a collection of open balls
A
It is opne
23
Q
If (A, d) is a metric subspace of (X, d). U is open in A =>
A
<=> (that is, every open set in a subspace is an intersection of the subspace and a set that is open in the larger space)
24
Q
2 metric ρ and d on same set X, are equivalent if (from balls)
A
<=>
25
Prove equivalence of 2 metrics on same set
26
Denote interior of A wrt (X,d)
