Complementary Pair of Quasi-antiorders

Siniš Crvenković,

Daniel Abraham Romano,

Melanija Mitrović

Abstrakt

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.

Słowa kluczowe: Constructive mathematics, set with apartness, anti-order, quasiantiorder, complementary pair of quasi-antiorders, half-space
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