Hello How to prove the min function is continuous?

[simpleeyelid]

Hello!

Could anybody give me an idea about this proof?

knowing f_{i}:X\rightarrowR i=1,2

to show whether f_{3}=min{f_{1},f_{2}} is continuous!

Thanks in advance,

Regards

 

[Office_Shredder]

Presumably f₁ and f₂ are continuous themselves? Is this a homework problem? I'll give you a small hint: work on the points where f₁(x)=/=f₂(x) and f₁(x)=f₂(x) separately

 

[simpleeyelid]

yeah, thanks, a lot, I finally find that it is convenient to construct it using the gluing lemma.

 

[tim_lou]

quick solution:

min(f, g) = (f+g)/2 - |f-g|/2