| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/topology/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 1 kB |
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Quelle composition_continuity.pvs Sprache: PVS |
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% Composition % % All references are to WA Sutherland "Introduction to Metric and % Topological Spaces", OUP, 1981 % % Author: David Lester, Manchester University, NIA, Université Perpignan % % Version 1.0 5/12/04 Initial Version % Version 1.1 8/6/06 Judgements added, Interface changed %------------------------------------------------------------------------------ composition_continuity[T1:Type,(IMPORTING topology_def[T1]) S:topology[T1], T2:Type,(IMPORTING topology_def[T2]) T:topology[T2], T3:Type,(IMPORTING topology_def[T3]) U:topology[T3]]: THEORY BEGIN IMPORTING continuity[T1,S,T2,T], continuity[T2,T,T3,U], continuity[T1,S,T3,U] f: VAR [T2->T3] g: VAR [T1->T2] x: VAR T1 composition_continuous_at: LEMMA continuous_at?(g,x) AND continuous_at?(f,g(x)) => continuous_at?(f o g, x) composition_continuous: LEMMA continuous?(g) AND continuous?(f) => continuous?(f o g) F: VAR continuous[T2,T,T3,U] G: VAR continuous[T1,S,T2,T] composition_is_continuous: JUDGEMENT o(F,G) HAS_TYPE continuous[T1,S,T3,U] END composition_continuity ¤ Dauer der Verarbeitung: 0.1 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28