Can a Continuous Bijection Have a Discontinuous Inverse?

  • Thread starter To0ta
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In summary, the conversation is about finding a function that meets certain criteria, specifically being one-to-one, onto, and continuous, with the added condition that its inverse is not continuous. One suggestion is the function e^x, but the question is not clearly stated.
  • #1
To0ta
6
0
find : E[tex]\subseteqR[/tex]

f : E[tex]\rightarrowR[/tex]

1_1 , onto , contonuo

such that

f[tex]^{}-1[/tex] : f(E) [tex]\rightarrowR[/tex]

is not continows

Please help me in finding a solution
 
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  • #2
Can you repost it such that it's more readable please?
 
  • #3
Perhaps you meant:

Let [itex]E\subseteq \mathbb{R}[/itex]. Find a function [itex]f : E\rightarrow \mathbb{R}[/itex] that is one-to-one, onto, and continuous such that [itex]f^{-1} : f(E) \rightarrow \mathbb{R}[/itex] is not continuous.

Is this your question?
 
  • #4
Yes, this is my question:smile:
 
  • #5
what about e^x?
 
  • #6
To0ta said:
Yes, this is my question:smile:

Why don't you just type your question? All of the stuff you are doing with special fonts, centering, and font size is distracting.
 

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