(2016). ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY. test, 45(2), 35-45. doi: 10.21608/aunj.2016.221419
. "ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY". test, 45, 2, 2016, 35-45. doi: 10.21608/aunj.2016.221419
(2016). 'ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY', test, 45(2), pp. 35-45. doi: 10.21608/aunj.2016.221419
ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY. test, 2016; 45(2): 35-45. doi: 10.21608/aunj.2016.221419

ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY

Assiut University Journal of Multidisciplinary Scientific Research
Volume 45, Issue 2, December 2016, Pages 35-45    PDF (546.69 K)
Document Type: Novel Research Articles
DOI: 10.21608/aunj.2016.221419
Abstract
In this paper, by using the power of nonstandard analysis tools, we review some of the standard facts on the intermediate value property (IVP) and investigates some new nonstandard developments by extending the classical definition. The notions are generalized to that of any real values; infinitesimals, infinitely close, unlimited. Finally, we give a nonstandard generalization of Sierpinski theorem. We prove that every function can be expressed as a sum of four discontinuous nonstandard functions with infinitesimal intermediate value property (IIVP).

Keywords
IVP; monad; galaxy; continuity; s-continuity; internal functions; Sierpinski
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