논문KCI 등재
A CONTINUOUS ONE-TO-ONE FUNCTION WHOSE INVERSE IS NOWHERE CONTINUOUS
한국수학교육학회|2011.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제18권 제2호|pp. 157-160
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Main purpose of this note is to construct an example of a continuous one-to-one function f : Q∗→ R whose inverse is nowhere continuous, and to show that the completeness is not necessary for the continuous inverse theorem.
Abstract
Main purpose of this note is to construct an example of a continuous one-to-one function f : Q∗→ R whose inverse is nowhere continuous, and to show that the completeness is not necessary for the continuous inverse theorem.
참고문헌 (5)
- T.M. Apostol, "Mathematical Analysis" (1974), Addison-Wesley
- R.G. Bartle, "Introduction to Real Analysis. 3rd Ed" (2000), John Wiley & Sons
- J. Dieudonne, "Foundations of Modern Analysis" (1969), Academic Press
- B. R. Gelbaum, "Counterexamples in Analysis" (1964), Holden-Day
- J. Lewin, "An Interactive Introduction to Mathematical Analysis" (2003), Cambridge University Press
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