Compatible Tight Riesz Orders II

Glass, A. M. W.

Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 304-307

Résumé

R. N. Ball (unpublished) and G. E. Davis and C. D. Fox [1] established that if Ω is a doubly homogeneous totally ordered set, the l-group A (Ω) of all orderpreserving permutations of Ω endures a compatible tight Riesz order. Specifically T = {g ∈ A(Ω)+ : supp (g) is dense in Ω} is a compatible tight Riesz order for A(Ω). Using this fact, I inserted Theorem 3.7 into [2; MR 53 (1977), #13070] at the galley proof stage. (It was also included in MR 54 (1977), #7350 and [3; p. 472].) Theorem 3.7 stated: Let Ω be homogeneous. Then A(Ω) endures a compatible tight Reisz order if and only if Ω is dense. I stated that it was obvious that if Ω were homogeneous and discrete, A(Ω) could not endure a compatible tight Riesz order. This “obvious” is neither obvious nor true.

Détail

DOI : 10.4153/CJM-1979-032-2

Bibliographie

[1] 1. Davis, G. E. and Fox, C. D., Compatible tight Riesz orders on the group of automorphisms of an 0-2 homogeneous set, Canadian J. Math.. 28 (1976), 1076–1081. Google Scholar

[2] 2. Glass, A. M. W., Compatible tight Riesz orders, Canadian J. Math.. 28 (1976), 186–200. Google Scholar

[3] 3. Glass, A. M. W., Ordered Permutation Groups, Bowling Green State University, 1976. Google Scholar

[4] 4. Reilly, N. R., Compatible tight Riesz orders and prime subgroups, Glasgow Math. J. 14 (1973), 146–160. Google Scholar