Singular Archimedean lattice-ordered groups |
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Authors: | A W Hager J Martinez |
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Institution: | (1) Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA, e-mail: martinez@math.ufl.edu, US;(2) Department of Mathematics, Wesleyan University, Middletown, CT 06459, USA, e-mail: ahager@eagle.wesleyan.edu, US |
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Abstract: | W stands for the category of all archimedean l-groups with designated weak unit. The subcategory W
s
of all groups with singular weak unit is analyzed as a full subcategory of W which is both epireflective and monocoreflective. A general technique for "contracting" monoreflections of a category A to a monocoreflective subcategory B is developed and then applied to W
s
to show that: (i) the projectable hull in W
s
is a monoreflection; (ii) essential hulls in W
s
are formed by simply taking the lateral completion, and G is essentially closed in this category if and only if , where X is compact, Hausdorff and extremally disconnected; (iii) the maximum monoreflection on W
s
, denoted , is obtained by contracting the maximum monoreflection on W, and G is epicomplete in W
s
precisely when G is laterally -complete; (iv) the maximum essential reflection on W
s
, denoted , is the contraction of the maximum essential reflection on W.
Received January 22, 1997; accepted in final form June 11, 1998. |
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Keywords: | |
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