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By Dr. Jacques Bair, Dr. René Fourneau (auth.)
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Nvexe, aCA = ciA nous d 4 d u i s o n s sans peine ; s i 1CA =E, iCA C CaA ; les CaA C iCA e t aCA < CiA ; s i CA est prcprement ~ convexe , ICA = C a A . 2. Liaisons e n t r e internat, partie non uniponctuelle m a r g e et a t t e n ~ n c e . - A d_~e E, aA = IAUmA tions, iA et mA p a r t i t i o n n e n t n'est vide. (~) Pour une g4n4ralisation, a) Pour une ; dans ces m@mes condi- aA si aucun de ces deux ensembles voir B a i r - J o n g m a n s [3]. 38 En effet, soit x un point = mA. R~ciproquement, ponctuel.
Lemme. Si %0 est une injection lin~aire de E dans' E' et si a,b sent des ~oints distincts de E' -I ( [ a : b [ ) De fait, : [$1(a) : ~1(b)[ [$1(a):$1(b)[ ~rx$1(a)+(1-x)$1(b)J _et _ J, ~1(]a:b[) C $1([a:b[) = ~a+(1-X)b : ]~1(a) : ~1(b)[ car ~ [a:b[ , O Comportement de la fermeture alg@brique r@u~ion, de l ' ~ n t e r s e c t • et des applications Ces relations = ~ A. 6. 55 Si k E iA N mB, B e s t une demi-droite point4e en k doric, puisque A est 4toil4 sur k, A 0 B e t un segment point~ en k ou une demi-droite point4e en k. De l&, f(AnB) est un segment point4 [k:l] ou une demi-droite point4e [k:l). 2. De l&, fA 0 fB = fA 0 B e s t un segment point4 (car alg4briquement ferm4) [k:t]ouur~demi-droite point4e [k:t). 1; or t E bA, donc [k:t[ ( IA ( A c e qui exige I = t.