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ISSN : 1226-0657

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Vol.18 No.2

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A CONTINUOUS ONE-TO-ONE FUNCTION WHOSE INVERSE IS NOWHERE CONTINUOUS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2011, v.18 no.2, pp.157-160
https://doi.org/10.7468/jksmeb.2011.18.2.157
Kim, Won-Kyu
Hong, Sun-Pyo
Kim,, W. , & Hong,, S. (2011). A CONTINUOUS ONE-TO-ONE FUNCTION WHOSE INVERSE IS NOWHERE CONTINUOUS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 18(2), 157-160, https://doi.org/10.7468/jksmeb.2011.18.2.157

Abstract

Main purpose of this note is to construct an example of a continuous one-to-one function f : <TEX>${\mathbb{Q}}^*{\rightarrow}{\mathbb{R}}$</TEX> whose inverse is nowhere continuous, and to show that the completeness is not necessary for the continuous inverse theorem.

keywords
continuous inverse function

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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