publication . Article . 2015

Topology from Neighbourhoods

Roland Coghetto;
Open Access
  • Published: 01 Dec 2015 Journal: Formalized Mathematics, volume 23, pages 289-296 (issn: 1426-2630, eissn: 1898-9934, Copyright policy)
  • Publisher: Walter de Gruyter GmbH
Abstract
<jats:title>Summary</jats:title> <jats:p>Using Mizar [9], and the formal topological space structure (<jats:monospace>FMT_Space_Str</jats:monospace>) [19], we introduce the three <jats:monospace>U-FMT</jats:monospace> conditions (<jats:monospace>U-FMT filter, U-FMT with point</jats:monospace> and <jats:monospace>U-FMT local</jats:monospace>) similar to those <jats:italic>V<jats:sub>I</jats:sub></jats:italic>, <jats:italic>V<jats:sub>II</jats:sub></jats:italic>, <jats:italic>V<jats:sub>III</jats:sub></jats:italic> and <jats:italic>V<jats:sub>IV</jats:sub></jats:italic> of the proposition 2 in [10]: <jats:disp-quote> <jats:p>If to each element <jats:italic>x</jats...
Subjects
free text keywords: Applied Mathematics, Computational Mathematics, 54A05, 03B35, filter, neighbourhoods system, identifier: FINTOPO7, version: 8.1.04 5.34.1256, QA1-939, Topological space, Neighbourhood system, Topology, Mathematics
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