Nonstandard Version of Intermediate Value Property
DOI:
https://doi.org/10.25271/2017.5.1.356Keywords:
IVP functions, CIVP functions, Functions with perfect road, Bair one functions, monad, s-continuityAbstract
In this paper, some new properties and results about Intermediate Value Property (IVP) via nonstandard concepts are given, and modifying some existing results to show the advantage role of nonstandard analysis tools for obtaining differed nonstandard distinguished results
References
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Banaszewski K.(1997). Algebraic properties of functions with the Cantor intermediate value property, Math. Slovaca 47.
Brown, J. B., Humke, P. and Laczkovich, M. (1988). Measurable Darboux functions, Proc. Amer. Math. Soc. 102 No.3, 603-610.
Bruckner, A. M.(1982). On factoring a function into a product of Darboux functions, Rend. Circ. Mat. Palermo 41, 16–22.
Bruckner, A. M., Bruckner, J. B. and Thomson, B. S.(1997). Real Analysis, Prentice-Hall, Inc.
Darboux, G. (1875). Memoire sur les fonctions discontinues, Ann. Sci. Scuola Norm. Sup. 4, 57–112.
Gibson, R. G. and Natkaniec, T. (1996-97). Darboux like functions, Real Anal. Exchange 22 No. 2,492-533.
Gibson, R. G. and Rouch, F. (1982). The Cantor intermediate valve property, Topol. Proc. 7, 55–62.
Goldblatt, R. (1998). Lectures on the Hyperreals: An Introduction to Nonstandard Analysis,Springer-Verlag New York, Inc.
Hurd, A. E. and Loeb, P. A. (1985). An Introduction to Nonstandard Real Analysis, Acadimic Press, New York.
Kuratowski, C. and Sierpinski, W. (1922). Les fonctions de classe 1 et les ensembles connexes punctiformes, Fund. Math. 3, 303–313.
Kusraev, A. G. and Kutateladze, S. S. (1994). Nonstandard Methods of Analysis, Kluwer Academic Publishers, Dordecht etc.
Maliszewski, A. (2006). Maximums of Darboux Baire one functions, Mathematica Slovaca 56, No. 4, 427–431.
Maximoff, I. (1936). Sur les fonctions ayant la propriété de Darboux, Prace Mat.-Fiz 43, 241-265.
Nelson, E. (1977). Internal set theory, a new approach to nonstandard analysis, Bull. Amer. Math. Soc. 83, No.6, 1165–1198.
Palmgren, E. (1998). Developments in constructive nonstandard analysis,The Bulletin of Symbolic Logic 4, No. 3, 233–272.
Pawlak, R. J. (1987). On rings of Darboux functions,Colloq. Math. 53, 283-300.
Robinson, A. (1970). Nonstandard Analysis, Second edition. North-Holland, Pub. Comp. Amsterdam.
Rosen, H. (2002/2003). Darboux symmetrically continuous functions, Real Analysis Exchange 28, No.2, 471–475.
Thomson, B. S. (1994). Symmetric properties of real functions, Marcel Dekker,Inc., New York.
Young, J. (1970). A theorem in the theory of functions of a real variable, Rend. Circ. Mat. Palermo 24 (1907),187–192. Second edition. North-Holland, Pub. Comp. Amsterdam.
Banaszewski K.(1997). Algebraic properties of functions with the Cantor intermediate value property, Math. Slovaca 47.
Brown, J. B., Humke, P. and Laczkovich, M. (1988). Measurable Darboux functions, Proc. Amer. Math. Soc. 102 No.3, 603-610.
Bruckner, A. M.(1982). On factoring a function into a product of Darboux functions, Rend. Circ. Mat. Palermo 41, 16–22.
Bruckner, A. M., Bruckner, J. B. and Thomson, B. S.(1997). Real Analysis, Prentice-Hall, Inc.
Darboux, G. (1875). Memoire sur les fonctions discontinues, Ann. Sci. Scuola Norm. Sup. 4, 57–112.
Gibson, R. G. and Natkaniec, T. (1996-97). Darboux like functions, Real Anal. Exchange 22 No. 2,492-533.
Gibson, R. G. and Rouch, F. (1982). The Cantor intermediate valve property, Topol. Proc. 7, 55–62.
Goldblatt, R. (1998). Lectures on the Hyperreals: An Introduction to Nonstandard Analysis,Springer-Verlag New York, Inc.
Hurd, A. E. and Loeb, P. A. (1985). An Introduction to Nonstandard Real Analysis, Acadimic Press, New York.
Kuratowski, C. and Sierpinski, W. (1922). Les fonctions de classe 1 et les ensembles connexes punctiformes, Fund. Math. 3, 303–313.
Kusraev, A. G. and Kutateladze, S. S. (1994). Nonstandard Methods of Analysis, Kluwer Academic Publishers, Dordecht etc.
Maliszewski, A. (2006). Maximums of Darboux Baire one functions, Mathematica Slovaca 56, No. 4, 427–431.
Maximoff, I. (1936). Sur les fonctions ayant la propriété de Darboux, Prace Mat.-Fiz 43, 241-265.
Nelson, E. (1977). Internal set theory, a new approach to nonstandard analysis, Bull. Amer. Math. Soc. 83, No.6, 1165–1198.
Palmgren, E. (1998). Developments in constructive nonstandard analysis,The Bulletin of Symbolic Logic 4, No. 3, 233–272.
Pawlak, R. J. (1987). On rings of Darboux functions,Colloq. Math. 53, 283-300.
Robinson, A. (1970). Nonstandard Analysis, Second edition. North-Holland, Pub. Comp. Amsterdam.
Rosen, H. (2002/2003). Darboux symmetrically continuous functions, Real Analysis Exchange 28, No.2, 471–475.
Thomson, B. S. (1994). Symmetric properties of real functions, Marcel Dekker,Inc., New York.
Young, J. (1970). A theorem in the theory of functions of a real variable, Rend. Circ. Mat. Palermo 24 (1907),187–192. Second edition. North-Holland, Pub. Comp. Amsterdam.
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Published
2017-03-30
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Hamad, I. O., & Hussein, S. A. (2017). Nonstandard Version of Intermediate Value Property. Science Journal of University of Zakho, 5(1), 142–146. https://doi.org/10.25271/2017.5.1.356
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Science Journal of University of Zakho
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