A relatively compact sets arbitrarily close to a set
$begingroup$
In a lot of papers for example (1) and (2), the authors use this technique: in order to prove that a set $V$ is relatively compact in a Banach space $X$, they construct a family of sets $V_delta$ such that $V_delta$ is relatively compact and $V_deltarightarrow V$ as $deltarightarrow 0$,
Therefore, there are relatively compact sets arbitrarily close to the set $V$.
Hence the set $V$ is also relatively compact in $X$.
I'm wondering why this is true?
real-analysis analysis compactness
asked Jan 14 at 14:52
MotakaMotaka
239111
$endgroup$
add a comment |
$begingroup$
In a lot of papers for example (1) and (2), the authors use this technique: in order to prove that a set $V$ is relatively compact in a Banach space $X$, they construct a family of sets $V_delta$ such that $V_delta$ is relatively compact and $V_deltarightarrow V$ as $deltarightarrow 0$,
Therefore, there are relatively compact sets arbitrarily close to the set $V$.
Hence the set $V$ is also relatively compact in $X$.
I'm wondering why this is true?
real-analysis analysis compactness
asked Jan 14 at 14:52
MotakaMotaka
239111
$endgroup$
add a comment |
$begingroup$
In a lot of papers for example (1) and (2), the authors use this technique: in order to prove that a set $V$ is relatively compact in a Banach space $X$, they construct a family of sets $V_delta$ such that $V_delta$ is relatively compact and $V_deltarightarrow V$ as $deltarightarrow 0$,
Therefore, there are relatively compact sets arbitrarily close to the set $V$.
Hence the set $V$ is also relatively compact in $X$.
I'm wondering why this is true?
real-analysis analysis compactness
asked Jan 14 at 14:52
MotakaMotaka
239111
$endgroup$
In a lot of papers for example (1) and (2), the authors use this technique: in order to prove that a set $V$ is relatively compact in a Banach space $X$, they construct a family of sets $V_delta$ such that $V_delta$ is relatively compact and $V_deltarightarrow V$ as $deltarightarrow 0$,
Therefore, there are relatively compact sets arbitrarily close to the set $V$.
Hence the set $V$ is also relatively compact in $X$.
I'm wondering why this is true?
real-analysis analysis compactness
real-analysis analysis compactness
asked Jan 14 at 14:52
MotakaMotaka
239111
asked Jan 14 at 14:52
MotakaMotaka
239111
asked Jan 14 at 14:52
MotakaMotaka
239111
asked Jan 14 at 14:52
MotakaMotaka
239111
asked Jan 14 at 14:52
MotakaMotaka
239111
239111
add a comment |
add a comment |
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