"Famille sommable" in English 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 $$(\forall \epsilon > 0) \, (\exists J_0 \in \mathcal F(I)) \, (\forall K \in \mathcal F(I \setminus J_0)) \, \left\Vert \displaystyle \sum_{k \in K} c_k \right\Vert< \epsilon$$ 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 causeUncountable sum of vectors in a Hilbert Space._

It's a "summable family". That's the expression that is used in the English version of Bourbaki's _General Topology_.