Abstract
We study the space \({{\mathrm{Max~}}}_d(G)\) of maximal d-subgroups of a lattice-ordered group, paying specific attention to archimedean \(\ell \)-groups with weak order unit. For such an object (G, u), \({{\mathrm{Max~}}}_d(G)\) lays at a level in between the space of minimal prime subgroups and the Yosida space of (G, u). Theorem 5.10 gives the appropriate generalization of a quasi F-space to W-objects which avoids a discussion of o-complete \(\ell \)-groups.
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Notes
\({\mathfrak {C}}(G)\) is the frame of convex \(\ell \)-subgroups of G.
BD(X) is the basically disconnected cover of Vermeer [24].
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Bhattacharjee, P., McGovern, W.W. Maximal d-subgroups and ultrafilters. Rend. Circ. Mat. Palermo, II. Ser 67, 421–440 (2018). https://doi.org/10.1007/s12215-017-0323-9
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DOI: https://doi.org/10.1007/s12215-017-0323-9