Counterexamples in Analysis

Volume 4, Issue 4, pp 523--526 http://dx.doi.org/10.22436/jmcs.04.04.02

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Authors

S. Alireza Jalili - Department of Mathematics, Omidiyeh Branch, Islamic Azad University, Omidiyeh , Iran Narges Khatoon Tohidi - Department of Mathematics, Omidiyeh Branch, Islamic Azad University, Omidiyeh , Iran

Abstract

The counterexamples are used for better comprehension of underlying concept in a theorem or definition. This paper is about the counterexamples in Mathematical Analysis, that we construct them to be apparently correct statements by a few change in the conditions of a valid proposition. Our aim in this paper is to present how the counterexamples help to boost the level of understanding of mathematical Analysis concepts.

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Keywords

• Counterexamples
• Topological Space
• Convergence
• Divergence.

MSC

•  54G20

References

• [1] P. Alexandrov, H. Hopf, Topologie, Springer, Berlin (1935)
  • View Article
  • Google Scholar


• [2] S. Banach , Theorie des operations lineaires, Instytut Matematyczny Polskiej Akademi Nauk, Germany (1932)
  • View Article
  • Google Scholar


• [3] N. Dunford, J. Schwartz, Linear operators, Interscience publishers, New York (1958)
  • View Article
  • Google Scholar


• [4] B. R. Gelbaum, J. M. H. Olmsted, Counterexamples in Analysis, Dover Holden-Day, Inc., 2003 (2003), San Francisco
  • View Article
  • Google Scholar


• [5] F. Hausdorff, Mengenlehre, Dover Publications, New York (1944)
  • Google Scholar


• [6] J. Mason, S. Klymchuk, Using counter-examples in calculus, World Scientific, New York (2009)
  • View Article
  • Google Scholar


• [7] M. I. A. Othman, A. M. S. Mahdy, Differential Transformation Method and Variation Iteration Method for Cauchy Reaction-diffusion Problems, The Journal of Mathematics and Computer Science, 1 (2010), 61--75
  • View Article
  • Google Scholar


• [8] J. Rashidinia, A. Tahmasebi, Taylor Series Method For The System Of Linear Volterra Integro-differential Equations, J. Math. Computer Sci., 4 (2012), 331--343
  • View Article
  • Google Scholar