Order representability in groups and vector spaces
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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http://dx.doi.org/10.1016/j.exmath.2012.01.007 |
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Title
Order representability in groups and vector spacesDate
2012Publisher
ElsevierISSN
0723-0869Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0723086912000084Version
info:eu-repo/semantics/publishedVersionAbstract
In the present paper, first we study in a systematic way the numerical representation problem for total preorders defined either on groups or on real vector spaces. Then, we consider groups and real vector spaces ... [+]
In the present paper, first we study in a systematic way the numerical representation problem for total preorders defined either on groups or on real vector spaces. Then, we consider groups and real vector spaces equipped with a topology, and analyze the fulfillment of the so-called continuous representability property; the latter meaning that every continuous total preorder defined on the given topological space admits a continuous real-valued order-preserving function. We also explore the analogous cases as above for total preorders that are compatible with the given algebraic structure, looking for real-valued, continuous or not, order-preserving functions that, in addition, are algebraic homomorphisms [-]
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Expositiones Mathematicae. 2012, Volume 30, Issue 2Rights
© 2012 Elsevier GmbH. All rights reserved.
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- MAT_Articles [764]