Thread: Metrics
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Old November 29th, 2008, 01:38 PM
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Quote:
Originally Posted by selinunan View Post
Let M be some nonempty set
a) Let d be a metric on M and P ∈ M; Q ∈ B (P, r) . Show that
B (Q, s) ⊂ B (P, r + s)

b) Let d be a metric on M and P,Q ∈ M, T ∈ B (P, r) ∩ B (Q, r) . Find
some s > 0 so that B (T, s) ⊂ B (P, r) ∩ B (Q, r)
a) Hint: If X \in B(Q;s) then d(P,X) \leq d(P,Q)+d(Q,X)

b) Hint: s=\frac {\min\{r-d(P,T),r-d(Q,T)\}}{2}
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