@MISC{CARDFIL3.MIZ,
  AUTHOR = {Coghetto, Roland},
  TITLE = {Summable family in a commutative group},
  DAY = {14},
  MONTH = {August},
  YEAR = {2015},
  ADDRESS1 = {Rue de la Brasserie 5\\7100 La Louvi\`ere, Belgium},
  SUMMARY = {H{\"o}lzl et al. showed that it was possible to build 
  ``a generic theory of limits based on filters" in Isabelle/HOL \cite{holzl2013type,boldo2014formalization} . 
  \par
  First, we compare the notions of limit of a family indexed 
  by a directed set, or a sequence, 
  in a metric space \cite{FRECHET.ABS}, a real normed linear space \cite{NORMSP_1.ABS} and 
  a linear topological space \cite{RLTOPSP1.ABS}
  with the concept of limit of image filter \cite{CARDFIL2.ABS}.  
  \par
  Then, following Bourbaki \cite{bourbaki2007topologie,bourbaki2013general} 
  (TG.III, \S 5.1 Familles 
  sommables dans un groupe commutatif),  we conclude by defining 
  the summable families in a commutative group (Additive notation 
  \cite{GROUP_1A.ABS}), using the notion of filters.}

  MSC2010 = {54A20 03B35},
  KEYWORDS = {convergence; summable family; filter; additive topological group}
}

@book{bourbaki2007topologie,
  title={Topologie g{\'e}n{\'e}rale: Chapitres 1 {\`a} 4},
  author={Bourbaki, N.},
  series={El{\'e}ments de math{\'e}matique},
  year={2007},
  publisher={Springer Science {\&} Business Media}
}


