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

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Additional resources 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

Wir betrachten topologischer geordneter topologischer erhilt die partielle In d e r S c h r e i b w e i s e C = P(~(M)) men geordneter b 1 = b 2 , ( a l , a 2 ) e d o m ( ^ A) Der I s o m o r p h i s m u s (bzw. Beweis. und falls : I. = AxC (aiAa2,b I ) R~ume aus §3 gilt die z u e i n a n d e r R~ume Operation A A = ~(L) (~(M)) inversen Isomorphis- 41 : ~(L) (~(M)) ~(a,c) aus Hilfssatz x x,y,z und y Elemente yon vergleichbar aus d e r M o n o t o n i e . Es (z',c3) sei Also ~(M) an, (x',c I) cI = c2 = c3 und (x',y') wie in G8 A dicht dab ist, A : .

Eine Kongruenz auf L und ist : L/I ~I^: L ÷ L/I A die Projektionsabbildung, ein injektiver, stetiger durchschnittsirreduziblen total unzusammenh~ngende so ~ s t ~l A-Homomorphismus. 3. der des Verbandes gekennzeichnet. L. DARSTELLUNGSSATZ. offenen jedes Jeder abqeschlossenen Ger~st offenen G Im folgenden eine ~(L)xP total sei DAS und gilt eine := kompakten ~(~(L)) isomorph des Verbandes Raum. O Kurz , und ~(G) aller : und I und P Operation falls A p=q Lp . Auf durch und (x,y)~dOm(A~(LI (x,p) falls (x,p) ~ (y,q) (y,q) falls (y,q) ~ (x,p) undefiniert sonst.

Anenh~n 39 L P ~ MQ s_~o g i b t es einen Zuerst das Verband G - G = GI+G 2 ist geordnete Mengen -- V B M -~ V C P -- C × D Q ~-' B × D wir die wenn und L untersuchen GerHst V , den Summe Begriff der G = GIOG 2 so, produktunzerlegbar. 2 LEMMA. Sind L,M und L genau dann Beweis. Man sieht ~- ~ ( M ) + ~ ( N ) leicht, Gilt mit dem jedoch = ~(~(M)) GuH ~ (G,H) ist. sein Ger~st des I Ein seien P Verband L und Mengen. dem und Q von sind ~(M) = MxN . folgt = ~(~(~(M)+~(N)))= genau dann ~(M)+~(N) produktunzerlegbar, wenn ist.

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