Homeomorphisms

[kiddopop]

Give an example of a function f:R to R (domain with the discrete topology; range with the standard topology), that is bijective and continuous, but not a homeomorphism.

I feel like f(x)=x^2 might satisfy this, but I'm not sure.

 

[daon2]

Is that function bijective? You want a function which is bijective and continuous but who's inverse is not.