Summable Family in a Commutative Group

Roland Coghetto

Formalized Mathematics (2015)

  • Volume: 23, Issue: 4, page 279-288
  • ISSN: 1426-2630

Abstract

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Hölzl et al. showed that it was possible to build “a generic theory of limits based on filters” in Isabelle/HOL [22], [7]. In this paper we present our formalization of this theory in Mizar [6]. First, we compare the notions of the limit of a family indexed by a directed set, or a sequence, in a metric space [30], a real normed linear space [29] and a linear topological space [14] with the concept of the limit of an image filter [16]. Then, following Bourbaki [9], [10] (TG.III, §5.1 Familles sommables dans un groupe commutatif), we conclude by defining the summable families in a commutative group (“additive notation” in [17]), using the notion of filters.

How to cite

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Roland Coghetto. "Summable Family in a Commutative Group." Formalized Mathematics 23.4 (2015): 279-288. <http://eudml.org/doc/276851>.

@article{RolandCoghetto2015,
abstract = {Hölzl et al. showed that it was possible to build “a generic theory of limits based on filters” in Isabelle/HOL [22], [7]. In this paper we present our formalization of this theory in Mizar [6]. First, we compare the notions of the limit of a family indexed by a directed set, or a sequence, in a metric space [30], a real normed linear space [29] and a linear topological space [14] with the concept of the limit of an image filter [16]. Then, following Bourbaki [9], [10] (TG.III, §5.1 Familles sommables dans un groupe commutatif), we conclude by defining the summable families in a commutative group (“additive notation” in [17]), using the notion of filters.},
author = {Roland Coghetto},
journal = {Formalized Mathematics},
keywords = {limits; filters; topological group; summable family; convergence series; linear topological space},
language = {eng},
number = {4},
pages = {279-288},
title = {Summable Family in a Commutative Group},
url = {http://eudml.org/doc/276851},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Roland Coghetto
TI - Summable Family in a Commutative Group
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 4
SP - 279
EP - 288
AB - Hölzl et al. showed that it was possible to build “a generic theory of limits based on filters” in Isabelle/HOL [22], [7]. In this paper we present our formalization of this theory in Mizar [6]. First, we compare the notions of the limit of a family indexed by a directed set, or a sequence, in a metric space [30], a real normed linear space [29] and a linear topological space [14] with the concept of the limit of an image filter [16]. Then, following Bourbaki [9], [10] (TG.III, §5.1 Familles sommables dans un groupe commutatif), we conclude by defining the summable families in a commutative group (“additive notation” in [17]), using the notion of filters.
LA - eng
KW - limits; filters; topological group; summable family; convergence series; linear topological space
UR - http://eudml.org/doc/276851
ER -

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