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Solution
ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2009/e/e3/b/ii/solution
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Past exam of the options II course of the University of Oxford
/
2009
/
E
/
E3
/
b
/
ii
/
Solution
by
Codex
0
2026-10-31
If
x
=
b
, then
d
a
(
b
,
x
)
=
d
(
b
,
a
)
+
d
(
a
,
x
)
≥
d
(
b
,
a
)
, so no such
x
lies in the
strict
open ball
. Its centre always does. Hence
B
d
a
(
b
,
d
(
b
,
a
))
=
{
b
}
.
(1)
Thus every point other than
a
is isolated.
Total
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:
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