It is true that if $f:\mathbb R \rightarrow \mathbb C$ is continuous on all the domain, then it cannot be bijective? How can I demonstrate this (or show a counter-example for it)?
Asked
Active
Viewed 223 times
0
-
See this question. It requires some pretty heavy theory AFAIK (I don't know how much analysis you've done) – Izaak van Dongen Feb 10 '20 at 16:31
-
What do you denote $R$ and $C$? – Bernard Feb 10 '20 at 16:31
-
@Bernard almost certainly $\mathbb R$ and $\mathbb C$, though perhaps OP will clarify that it's not – Izaak van Dongen Feb 10 '20 at 16:32
-
Sorry, obviously i meant real and complex numbers, anyway I edited so now it is more clear – user720386 Feb 10 '20 at 16:35
-
1@IzaakvanDongen Thank you very much now it is quite clear :) – user720386 Feb 10 '20 at 16:38