If is continuous at in the definition of continuity use .
It follows that for all near .
The question is as follows:
Let f:R->R be continuous. Show that {x:f(x)>0} is an open subset of R.
I have figured out how to prove {x:f(x)=0} is a closed subset of R, but I can not solve the question {x:f(x)>0} is an open one.
Any help for that?
Thanks.