“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.










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  • $begingroup$
    en.wikipedia.org/wiki/… ?
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    – Clement C.
    Jan 4 at 11:02
















3












$begingroup$


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.










share|cite|improve this question









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  • $begingroup$
    en.wikipedia.org/wiki/… ?
    $endgroup$
    – Clement C.
    Jan 4 at 11:02














3












3








3





$begingroup$


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.










share|cite|improve this question









$endgroup$




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






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asked Jan 4 at 10:58









mathcounterexamples.netmathcounterexamples.net

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  • $begingroup$
    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




$begingroup$
en.wikipedia.org/wiki/… ?
$endgroup$
– Clement C.
Jan 4 at 11:02










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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.






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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.






    share|cite|improve this 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.






      share|cite|improve this 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.






        share|cite|improve this answer









        $endgroup$



        It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.







        share|cite|improve this answer












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        answered Jan 4 at 11:06









        José Carlos SantosJosé Carlos Santos

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