Weakly Isotone and Strongly Reverse Isotone Mappings of Relational Systems
Abstract
The setting of this article is Classical algebra and Bishop's con-structive algebra (the algebra based on the Intuitionistic logic). The Esakia's concept in the classical mathematics of strongly isotone mapping between ordered sets is extended onto two different concepts of mappings: on the concept of weakly isotone and the concept of strongly reverse isotone mapping of rela-
tional systems. Some characterizations of those mappings are given and some application of those mappings in ordered semigroup theory are given.
References
[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] D. S. Bridges and L.S.Vita: Techniques of constructive analysis, Springer, New York 2006.
[4] J. Chvalina: The Iski-type characterization of certain regular ordered semigroups; Czechosl. Math. J., 47(2)(1997), 261-276.
[5] S. Crvenkovic, M. Mitrovic and D. A. Romano: Semigroups with Apartness; Math. Logic Quart., 59(6)(2013), 407-414.
[6] L. L. Esakia: O topologiceskich modeljach Kripke [On topological Kripke models]. Dokl. AN SSSR 214(2)(1974), 298-301.
[7] A. Heyting: Intuitionism. An Introduction. North-Holland, Amsterdam, 1956.
[8] R. Mines, F. Richman and W. Ruitenburg: A Course of constructive algebra, Springer, New York 1988.
[9] D. A. Romano: A note on quasi-antiorder in semigroup; Novi Sad J. Math., 37(1) (2007), 3-8.
[10] D.A.Romano: A Remark on Mapping between Relational Systems; In Pilipovic, S. (ed.) Proceedings of the 12th Serbian Mathematical Congress (August 28 - September 03, 2008),
(pp. 13-17), Department of Mathenmatics, University Novi Sad, 2011.
[11] D. A. Romano: On Quasi-Antiorder Relation on Semigroups; Mat. vesnik, 64(3)(2012), 190-199.
[12] D. A. Romano: On some mappings between co-quasiordered relational systems; Bull.Inter. Math. Virt. Inst., 7(2)(2017), 279{291.
[13] A. S. Troelstra and D. van Dalen: Constructivism in mathematics, An introduction; North-Holland, Amsterdam 1988.
[2] D. S. Bridges and F. Richman, Varieties of constructive mathematics, London Mathematical Society Lecture Notes 97, Cambridge University Press, Cambridge, 1987.
[3] D. S. Bridges and L.S.Vita: Techniques of constructive analysis, Springer, New York 2006.
[4] J. Chvalina: The Iski-type characterization of certain regular ordered semigroups; Czechosl. Math. J., 47(2)(1997), 261-276.
[5] S. Crvenkovic, M. Mitrovic and D. A. Romano: Semigroups with Apartness; Math. Logic Quart., 59(6)(2013), 407-414.
[6] L. L. Esakia: O topologiceskich modeljach Kripke [On topological Kripke models]. Dokl. AN SSSR 214(2)(1974), 298-301.
[7] A. Heyting: Intuitionism. An Introduction. North-Holland, Amsterdam, 1956.
[8] R. Mines, F. Richman and W. Ruitenburg: A Course of constructive algebra, Springer, New York 1988.
[9] D. A. Romano: A note on quasi-antiorder in semigroup; Novi Sad J. Math., 37(1) (2007), 3-8.
[10] D.A.Romano: A Remark on Mapping between Relational Systems; In Pilipovic, S. (ed.) Proceedings of the 12th Serbian Mathematical Congress (August 28 - September 03, 2008),
(pp. 13-17), Department of Mathenmatics, University Novi Sad, 2011.
[11] D. A. Romano: On Quasi-Antiorder Relation on Semigroups; Mat. vesnik, 64(3)(2012), 190-199.
[12] D. A. Romano: On some mappings between co-quasiordered relational systems; Bull.Inter. Math. Virt. Inst., 7(2)(2017), 279{291.
[13] A. S. Troelstra and D. van Dalen: Constructivism in mathematics, An introduction; North-Holland, Amsterdam 1988.
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2016-12-29
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