Tuesday, 20 December 2016

analysis - Is there a continuous function from [0,1] onto (0,1)?




If there is none, why?



And for the other side, what about open set (0,1) to closed set [0,1] with a continuous function?



Thanks


Answer



HINT: For the first one use the fact that, Continuous image of a compact set is compact.


-

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh→0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...