Complementary Pair of Quasi-antiorders
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The aims of the present paper are to introduction and investigate of notions of complementary pairs of quasi-antiorders and half-space quasi-antiorder on a given set. For a pair α and β of quasi-antiorders on a given set A we say that they are complementary pair if α ∪ β =6=A and α ∩ β = ∅. In that case, α (and β ) is called half-space on A. Assertion, if α is a half-space quasi-antiorder on A, then the induced anti-order θ on A/(α ∪ α−1) is a half-space too, is the main result of this paper.
07 - 07 - 2015
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