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221419

ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY

Article

Last updated: 28 Dec 2024

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Subjects

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Tags

Mathematics and Computer Science

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).

DOI

10.21608/aunj.2016.221419

Keywords

IVP, monad, galaxy, Continuity, s-continuity, internal functions, Sierpinski

Volume

45

Article Issue

2

Related Issue

31577

Issue Date

2016-12-01

Receive Date

2022-02-23

Publish Date

2016-12-01

Page Start

35

Page End

45

Print ISSN

2812-5029

Online ISSN

2812-5037

Article File

AUNJ_Volume 45_Issue 2_Pages 35-45.pdf

PDF . 559.8kB

Link

https://aunj.journals.ekb.eg/article_221419.html

Detail API

https://aunj.journals.ekb.eg/service?article_code=221419

Order

221,419

Type

Novel Research Articles

Type Code

2,242

Publication Type

Journal

Publication Title

Assiut University Journal of Multidisciplinary Scientific Research

Publication Link

https://aunj.journals.ekb.eg/

MainTitle

ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY

Details

Type

Article

Created At

23 Jan 2023