Open vs. connected subsets

[lmtuan]

yup. You can see it in the Battle's book about Real Analysis.

[anushrimali]

Originally Posted by lime

Hi! That is really buffling question for me as well, but I cannot understand another variant:

*by the way the question was about (0,1) not [0,1].

WHY? If f=tan(Pi/2*(x-0.5)) so in that case we have (0,1)->(-inf, +inf) and it is not bounded? Where am I wrong?

lime, (0,1) doesnt map to (-inf,+inf) with that function. the range is (-inf,1). Substitute x=1 and you will get f= tan (pi/2*1/2)= tan (pi/4)=1.

[lime]

Originally Posted by anushrimali

lime, (0,1) doesnt map to (-inf,+inf) with that function. the range is (-inf,1). Substitute x=1 and you will get f= tan (pi/2*1/2)= tan (pi/4)=1.

My bad. I meant f(x)=(Pi)(x-1/2).
Anyway, I understand where I was wrong. So never mind.