“Famille sommable” in English
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In French, given a normed vector space $(E, Vert cdot Vert)$, we say that a set of vectors $mathcal C = {c_i ; i in I}$ is a "famille sommable" when
$$(forall epsilon > 0) , (exists J_0 in mathcal F(I)) , (forall K in mathcal F(I setminus J_0)) , leftVert displaystyle sum_{k in K} c_k rightVert< epsilon$$
where $mathcal F(A)$ is defined as the sets of finite subsets of $A$.
Is there a similar wording in English? At least Wikipedia page I provided above is not refering to a similar an English page.
Note: this question has for root cause Uncountable sum of vectors in a Hilbert Space.
sequences-and-series terminology
asked Jan 4 at 10:58
mathcounterexamples.netmathcounterexamples.net
27k22157
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add a comment |
$begingroup$
In French, given a normed vector space $(E, Vert cdot Vert)$, we say that a set of vectors $mathcal C = {c_i ; i in I}$ is a "famille sommable" when
$$(forall epsilon > 0) , (exists J_0 in mathcal F(I)) , (forall K in mathcal F(I setminus J_0)) , leftVert displaystyle sum_{k in K} c_k rightVert< epsilon$$
where $mathcal F(A)$ is defined as the sets of finite subsets of $A$.
Is there a similar wording in English? At least Wikipedia page I provided above is not refering to a similar an English page.
Note: this question has for root cause Uncountable sum of vectors in a Hilbert Space.
sequences-and-series terminology
asked Jan 4 at 10:58
mathcounterexamples.netmathcounterexamples.net
27k22157
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$begingroup$
en.wikipedia.org/wiki/… ?
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– Clement C.
Jan 4 at 11:02
add a comment |
$begingroup$
In French, given a normed vector space $(E, Vert cdot Vert)$, we say that a set of vectors $mathcal C = {c_i ; i in I}$ is a "famille sommable" when
$$(forall epsilon > 0) , (exists J_0 in mathcal F(I)) , (forall K in mathcal F(I setminus J_0)) , leftVert displaystyle sum_{k in K} c_k rightVert< epsilon$$
where $mathcal F(A)$ is defined as the sets of finite subsets of $A$.
Is there a similar wording in English? At least Wikipedia page I provided above is not refering to a similar an English page.
Note: this question has for root cause Uncountable sum of vectors in a Hilbert Space.
sequences-and-series terminology
asked Jan 4 at 10:58
mathcounterexamples.netmathcounterexamples.net
27k22157
$endgroup$
In French, given a normed vector space $(E, Vert cdot Vert)$, we say that a set of vectors $mathcal C = {c_i ; i in I}$ is a "famille sommable" when
$$(forall epsilon > 0) , (exists J_0 in mathcal F(I)) , (forall K in mathcal F(I setminus J_0)) , leftVert displaystyle sum_{k in K} c_k rightVert< epsilon$$
where $mathcal F(A)$ is defined as the sets of finite subsets of $A$.
Is there a similar wording in English? At least Wikipedia page I provided above is not refering to a similar an English page.
Note: this question has for root cause Uncountable sum of vectors in a Hilbert Space.
sequences-and-series terminology
sequences-and-series terminology
asked Jan 4 at 10:58
mathcounterexamples.netmathcounterexamples.net
27k22157
asked Jan 4 at 10:58
mathcounterexamples.netmathcounterexamples.net
27k22157
asked Jan 4 at 10:58
mathcounterexamples.netmathcounterexamples.net
27k22157
asked Jan 4 at 10:58
mathcounterexamples.netmathcounterexamples.net
27k22157
asked Jan 4 at 10:58
mathcounterexamples.netmathcounterexamples.net
27k22157
27k22157
$begingroup$
en.wikipedia.org/wiki/… ?
$endgroup$
– Clement C.
Jan 4 at 11:02
add a comment |
$begingroup$
en.wikipedia.org/wiki/… ?
$endgroup$
– Clement C.
Jan 4 at 11:02
$begingroup$
en.wikipedia.org/wiki/… ?
$endgroup$
– Clement C.
Jan 4 at 11:02
$begingroup$
en.wikipedia.org/wiki/… ?
$endgroup$
– Clement C.
Jan 4 at 11:02
add a comment |
1 Answer
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It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered Jan 4 at 11:06
José Carlos SantosJosé Carlos Santos
165k22132235
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1 Answer
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$begingroup$
It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered Jan 4 at 11:06
José Carlos SantosJosé Carlos Santos
165k22132235
$endgroup$
add a comment |
$begingroup$
It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered Jan 4 at 11:06
José Carlos SantosJosé Carlos Santos
165k22132235
$endgroup$
add a comment |
$begingroup$
It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered Jan 4 at 11:06
José Carlos SantosJosé Carlos Santos
165k22132235
$endgroup$
It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered Jan 4 at 11:06
José Carlos SantosJosé Carlos Santos
165k22132235
answered Jan 4 at 11:06
José Carlos SantosJosé Carlos Santos
165k22132235
answered Jan 4 at 11:06
José Carlos SantosJosé Carlos Santos
165k22132235
answered Jan 4 at 11:06
José Carlos SantosJosé Carlos Santos
165k22132235
165k22132235
add a comment |
add a comment |
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en.wikipedia.org/wiki/… ?
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– Clement C.
Jan 4 at 11:02