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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.18 No.2

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

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

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2011, v.18 no.2, pp.157-160
https://doi.org/10.7468/jksmeb.2011.18.2.157
Kim, Won-Kyu (Department of Mathematics Education, Chungbuk National University)
Hong, Sun-Pyo (Department of Mathematics Education, Chungbuk National University)
Kim, Won-Kyu, & Hong, Sun-Pyo. (2011). A CONTINUOUS ONE-TO-ONE FUNCTION WHOSE INVERSE IS NOWHERE CONTINUOUS. , 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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한국수학교육학회지시리즈B:순수및응용수학

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