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Miklós Schweitzer
1995 Miklós Schweitzer
10
10
Part of
1995 Miklós Schweitzer
Problems
(1)
analysis
Source: miklos schweitzer 1995 q10
10/2/2021
Let
X
=
{
X
1
,
X
2
,
.
.
.
}
X =\{ X_1 , X_2 , ...\}
X
=
{
X
1
,
X
2
,
...
}
be a countable set of points in space. Show that there is a positive sequence
{
a
k
}
\{a_k\}
{
a
k
}
such that for any point
Z
∉
X
Z\not\in X
Z
∈
X
the distance between the point Z and the set
{
X
1
,
X
2
,
.
.
.
,
X
k
}
\{X_1,X_2 , ...,X_k\}
{
X
1
,
X
2
,
...
,
X
k
}
is at least
a
k
a_k
a
k
for infinitely many k.
geometry
real analysis