{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T16:39:51Z","timestamp":1648658391853},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2015,12,1]],"date-time":"2015-12-01T00:00:00Z","timestamp":1448928000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-sa\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>H\u00f6lzl et al. showed that it was possible to build \u201ca generic theory of limits based on filters\u201d in Isabelle\/HOL [22], [7]. In this paper we present our formalization of this theory in Mizar [6].<\/jats:p>\n               <jats:p>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].<\/jats:p>\n               <jats:p>Then, following Bourbaki [9], [10] (TG.III, \u00a75.1 <jats:italic>Familles sommables dans un groupe commutatif<\/jats:italic>), we conclude by defining the summable families in a commutative group (\u201cadditive notation\u201d in [17]), using the notion of filters.<\/jats:p>","DOI":"10.1515\/forma-2015-0022","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T23:40:48Z","timestamp":1459381248000},"page":"279-288","source":"Crossref","is-referenced-by-count":1,"title":["Summable Family in a Commutative Group"],"prefix":"10.1515","volume":"23","author":[{"given":"Roland","family":"Coghetto","sequence":"first","affiliation":[{"name":"Rue de la Brasserie 5, 7100 La Louvi\u00e8re, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,3,25]]},"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/23\/4\/article-p279.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2015-0022","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T08:16:19Z","timestamp":1617783379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2015-0022"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,1]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,3,25]]},"published-print":{"date-parts":[[2015,12,1]]}},"alternative-id":["10.1515\/forma-2015-0022"],"URL":"https:\/\/doi.org\/10.1515\/forma-2015-0022","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2015,12,1]]}}}