The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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A CONTINUOUS ONE-TO-ONE FUNCTION WHOSE INVERSE IS NOWHERE CONTINUOUS

  • Kim, Won-Kyu (Department of Mathematics Education, Chungbuk National University) ;
  • Hong, Sun-Pyo (Department of Mathematics Education, Chungbuk National University)
  • Received : 2011.02.24
  • Accepted : 2011.04.29
  • Published : 2011.05.31
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Abstract

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

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References

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