Metrics question

  • Thread starter thraxrules
  • Start date
  • #1
Can anyone prove this theorem please?
let (X,d) be a metric space, let [tex]x \in X[/tex] , and let [tex] 0<\delta<\epsilon [/tex]. Then cl(B(x,delta)) [tex] \subset [/tex]B(x,epsilon)
 
Last edited:

Answers and Replies

  • #2
125
0
Assume otherwise that is chose some y that is in the closure of B(x, eps) but is not in B(x, delt). Now use the triangle inequality that is required of the metric.
 

Related Threads on Metrics question

  • Last Post
Replies
11
Views
11K
Replies
17
Views
1K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
8
Views
352
T
  • Last Post
Replies
5
Views
959
Replies
3
Views
2K
Replies
22
Views
1K
Replies
2
Views
807
Top