hi guys, I have the following question. I know that an increasing function has only a countable number of points where it is discontinuous. My question is, is any increasing function upper semicontinuous in all its support?

Question

anonymous · Answer

any help? somebody?

anonymous · Answer

what is upper semicontinuous

anonymous · Answer

$$f(x)=\lfloor x \rfloor$$
is upper semicontinuous for x in R

anonymous · Answer

$$f(x)=x+\lfloor x \rfloor$$
 is an increasing function upper semicontinuous in all its support

anonymous · Answer

thanks guys. The point is that an increasing function has only countably many points of discontinuity but given that is increasing the function must take the value of the upper limit at any of these points. Hence, I thought this is sufficient to claim that any increasing function is upper semicontinuous, am I correct?

anonymous · Answer

u r right