Complementary Pair of Quasi-antiorders

Siniš Crvenković,

Daniel Abraham Romano,

Melanija Mitrović


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
[1] E. Bishop, Foundations of constructive analysis, McGraw-Hill, New York 1967.
[2] D. S. Bridges and F. Richman, Varieties of constructive mathematics, London Mathematical Society Lecture Notes 97, Cambridge University Press, Cambridge, 1987.
[3] I. Cajda, Congruences in transitive relational systems, Miscolc Math. Notes 5 (1) (2004), pp. 19–23.
[4] D. Joji´c and D.A.Romano, Quasi-antiorder relational systems, Inter. J. Contem. Math. Sciences 3 (27) (2008), pp. 1307–1315.
[5] A.I. Maltsev, Algebraic systems, Springer - Verlag, Berlin, 1973.
[6] R. Mines, F. Richman and W. Ruitenburg, A course of constructive algebra, Springer, New York 1988.
[7] D.A. Romano, On construction of maximal coequality relation and its applications, Proceedings of 8th international conference on Logic and Computers Sciences ”LIRA ’97”, Novi Sad, September 1-4, 1997, (Editors: R.Toˇsi´c and Z.Budimac), Institute of Mathematics, Novi Sad 1997, pp. 225–230.
[8] D.A. Romano, Some relations and subsets of semigroup with apartness generated by the principal consistent subsets, Univ. Beograd, Publ. Elektroteh. Fak. Ser. Math. 13 (2002), pp. 7–25.
[9] D.A. Romano, A note on quasi-antiorder in semigroup, Novi Sad J. Math. 37 (1) (2007), pp. 3–8.
[10] D.A. Romano, On regular anticongruence in anti-ordered semigroups, Publications de l’Institut Mathematique 81 (95) (2007), pp. 95–102.
[11] D.A. Romano, An isomorphism theorem for anti-ordered sets, Filomat 22 (1) (2008), pp. 145–160.
[12] A.S. Troelstra and D. van Dalen, Constructivism in mathematics, an Introduction, North-Holland, Amsterdam 1988.

Czasopismo ukazuje się w sposób ciągły on-line.
Pierwotną formą czasopisma jest wersja elektroniczna.