# On Some Mappings between Co-quasiordered Relational Systems

## Abstract

The setting of this article is Bishop's constructive mathematics.The connections between the strong mappings, U-mappings and L-mappings of co-quasiorder relational systems we analyzed. The relations between the strong mappings of co-quasiorder relational systems dened by Novotny and other mappings are also analysed. Finally, a new mapping between two relational systems is introduced. Some properties of these mappings and connection of

these mappings to the other known mappings are investigated.

## References

[1] Bishop, E. Foundations of constructive analysis. New York, NY: McGraw-Hill, 1967.

[2] Bridges, D. S. and Richman, F. Varieties of constructive mathematics. Cambridge: Cambridge University Press, 1987.

[3] Bridges, D. S. and Vita, L. S. Techniques of Constructive Analysis. Berlin: Springer, 2006.

[4] Bridges, D. S. and Vita, L. S. Apartness and Uniformity - A Constructive Development. Berlin: Springer, 2011.

[5] Chajda, I. and Hoskova, S. A characterization of cone preserving mappings of quasiordered sets. Miscols Math. Notes, 6(2005), 147-152.

[6] Crvenkovic, S., Mitrovic, M. and Romano, D. A. Semigroups with Apartness. Math. Logic Quarterly, 59(2013), 407-414.

[7] Crvenkovic, S., Mitrovic, M. and Romano, D. A. Notions of (Constructive) Semigroups with Apartness. Semigroup Forum, 92(2016), 659-674.

[8] Halas, R. and Hort, D. A characterisation of 1-, 2-, 3-, 4-homomorphisms of ordered sets. Czechoslovak Math. J., 53(2003), 213-221.

[9] Heyting, A. Intuitionism. An Introduction. Amsterdam: North-Holland, 1956.

[10] Jojic, J. and Romano, D. A. Quasi-antiorder relational system. International J. Contemp. Math. Sci., 3(2008), 1307-1315.

[11] Kortesi, P., Radeleczki, S. and Szilagyi, Sz. Congruences and isotone maps on partially ordered sets. Math. Pannonica, 16(2005), 39-55.

[12] Maltsev, A. I. On the general theory of algebraic systems., Matematiceskii Sbornik (N.S.), 35(77)(1954):1, 3-20.

[13] Mines, R., Richman, F. and Ruitenburg, R. A Course of Constructive Algebra. New York, NY: Springer, 1988.

[14] Novotny, M. Construction of all strong homomorphism of binary structures. Czechoslovak Math. J., 41(1991), 300-311.

[15] D. A. Romano. A note on quasi-antiorder in semigroup. Novi Sad J. Math., 37(2007), 3-8.

[16] Romano, D. A. A remark on mapping between relational systems; Paper presented at the 12th Serbian Mathematical Congress. Serbia: Novi Sad, 2008.

[17] Romano, D. A. On quasi-antiorder relation on semigroups. Mat. vesnik, 64(2012), 190-199.

[18] Ruitenburg, W. Intuitionistic Algebra (Unpublished doctoral dissertation). the Netherlands: University of Utrecht, 1982.

[19] Shum, K. P., Zhu, P. and Kehayopulu, N. II-homomorphism and III-congruences on posets. Discrete Math., 308(2008), 5006-5012.

[20] Troelstra, A. S. and van Dalen, D. Constructivism in Mathematics, An Introduction. Amsterdam: North-Holland, 1988.

[21] Vagner, V.V. Intro-restrictive factored and bi-factored ordered sets; Soviet Mathematics (Izvestiya VUZ. Matematika), 22(1978), 24-34

[2] Bridges, D. S. and Richman, F. Varieties of constructive mathematics. Cambridge: Cambridge University Press, 1987.

[3] Bridges, D. S. and Vita, L. S. Techniques of Constructive Analysis. Berlin: Springer, 2006.

[4] Bridges, D. S. and Vita, L. S. Apartness and Uniformity - A Constructive Development. Berlin: Springer, 2011.

[5] Chajda, I. and Hoskova, S. A characterization of cone preserving mappings of quasiordered sets. Miscols Math. Notes, 6(2005), 147-152.

[6] Crvenkovic, S., Mitrovic, M. and Romano, D. A. Semigroups with Apartness. Math. Logic Quarterly, 59(2013), 407-414.

[7] Crvenkovic, S., Mitrovic, M. and Romano, D. A. Notions of (Constructive) Semigroups with Apartness. Semigroup Forum, 92(2016), 659-674.

[8] Halas, R. and Hort, D. A characterisation of 1-, 2-, 3-, 4-homomorphisms of ordered sets. Czechoslovak Math. J., 53(2003), 213-221.

[9] Heyting, A. Intuitionism. An Introduction. Amsterdam: North-Holland, 1956.

[10] Jojic, J. and Romano, D. A. Quasi-antiorder relational system. International J. Contemp. Math. Sci., 3(2008), 1307-1315.

[11] Kortesi, P., Radeleczki, S. and Szilagyi, Sz. Congruences and isotone maps on partially ordered sets. Math. Pannonica, 16(2005), 39-55.

[12] Maltsev, A. I. On the general theory of algebraic systems., Matematiceskii Sbornik (N.S.), 35(77)(1954):1, 3-20.

[13] Mines, R., Richman, F. and Ruitenburg, R. A Course of Constructive Algebra. New York, NY: Springer, 1988.

[14] Novotny, M. Construction of all strong homomorphism of binary structures. Czechoslovak Math. J., 41(1991), 300-311.

[15] D. A. Romano. A note on quasi-antiorder in semigroup. Novi Sad J. Math., 37(2007), 3-8.

[16] Romano, D. A. A remark on mapping between relational systems; Paper presented at the 12th Serbian Mathematical Congress. Serbia: Novi Sad, 2008.

[17] Romano, D. A. On quasi-antiorder relation on semigroups. Mat. vesnik, 64(2012), 190-199.

[18] Ruitenburg, W. Intuitionistic Algebra (Unpublished doctoral dissertation). the Netherlands: University of Utrecht, 1982.

[19] Shum, K. P., Zhu, P. and Kehayopulu, N. II-homomorphism and III-congruences on posets. Discrete Math., 308(2008), 5006-5012.

[20] Troelstra, A. S. and van Dalen, D. Constructivism in Mathematics, An Introduction. Amsterdam: North-Holland, 1988.

[21] Vagner, V.V. Intro-restrictive factored and bi-factored ordered sets; Soviet Mathematics (Izvestiya VUZ. Matematika), 22(1978), 24-34

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## Published

2016-12-29

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