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By Bernhard Banaschewski (auth.), Bernhard Banaschewski, Rudolf-Eberhard Hoffmann (eds.)

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Additional info for Continuous Lattices: Proceedings of the Conference on Topological and Categorical Aspects of Continuous Lattices (Workshop IV) Held at the University of Bremen, Germany, November 9–11, 1979

Example text

4 : Folgerung und hat. (***) yon irreduzibler Ein K~rzungssatz (B) es fur e i n e n V e r b a n d (**) es e i n e n V e r b a n d fur P r o d u k t e einen wir ebenfalls dann nicht , die liefert was wir den VerWenn die Eigenschaft sind, der Voraussetzung Produkt mit der L = VB M haben verwendet. 2. (Duffus, mit LEMMA O und ist yon P H mit O J6nsson, eine , so s o l l I(H) den Verband aller bezeichnen. Rival endliche I ( H P) = [lo]). geordnete (I(H)) p Ist H Menge, ein V-Halbverband so gilt: 43 D.

Und of p a r t i a l l y [3] Gierz, Hashimoto, [6] Z. J. sets. Jbnsson, sets I. Rival ordered Math. ordered [5] 150 Ann. K~hler, sets. Math. L. : Topology [8] Stralka, A. R. Priestley R. , Technische Mathematik Hochschule DARMSTADT and Canad. properties. ordered Preprint. und K ~ r z u n g s - Darmstadt, Van Nostrand, ordered Forum of p a r t i a l l y of p a r t i a l l y 1979. 1965. space w h i c h is not a (to appear). and r e f i n e m e n t J. Math. B. J ~ n s s o n lattices, Fachbereich D-61 Semigroup yon Ver- 315-318.

Und S ( ~ I) T(D<) fdr T(~I) und T(-~I) folgt = E(Po, q) wollen besagt, (pn,qn)= wir := E(Po,qi) von (po,q) so gibt, und s c h l i e B e n und (pl,ql), i = I .... ,n wiederum (ui'vi)-~l dab dab fur aus S(-~I) (ui'vi+1) S(-~I) (ui,v i) fHr folgt w e g e n (po,q~) h a b e n wit nun e r s e t z t . Nach zeigen, dab es P a a r e -~I E(Pi,qi) i = o,1 .... ,n n und (u,v) E -I (ui_ 1,v i) = V Man v e r i f i z i e r t das G l e i c h h e i t s z e i c h e n -~I (ui'vi+1) (ui_1,vi_1)--~l i = I ..... n , durch kann man bewiesene und g e l t e n T(Px+I ) (Ui-l'Vi) -~I (ui'vi) Aus Eigenschaft (p * ,q * ) := E -I (Uo,V) (ui,vi) und d a r a u s es S(DX+I) (Uo'Vo) E(Pi_1,qi_1) setzen zu zeigen.

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