The Converse of the Heine-borel Theorem in a Riesz Domain
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چکیده
Then cuIi = 0. Hence every c -̂Ii = 0, Ji = L44. But Ii is free of At. Hence h = Ö, I = 0, £ = 0. THEOREM. Every linear covariant of q± is a linear function ofL,A4L,KL. Next, let co > 1. After subtracting from C a constant multiple of qJJ*", whose leader is b^u, we have d = 0 in S. Express S± as a polynomial in c^, cw, fei, and call p the coefficient of their product. The coefficient of c^Cis in S[ — Si = S, found from (1), is p(b4 + ci4), and hence vanishes if h = Cu; while # itself vanishes if also c24 = c34 == 0. Applying these two conditions to S = I + 64/i, we find that
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