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Lebl-Basic-Analysis-I
· Problem 7.3.9
Metric Spaces
Mathematics · sequences-and-convergence
Problem
Let
E
⊂
X
E \subset X
E
⊂
X
be closed and let
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
be a sequence in
X
X
X
converging to
p
∈
X
p \in X
p
∈
X
. Suppose
x
n
∈
E
x_n \in E
x
n
∈
E
for infinitely many
n
∈
N
n \in \mathbb{N}
n
∈
N
. Show
p
∈
E
p \in E
p
∈
E
.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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