All Questions
2
questions
2
votes
1
answer
195
views
Is this an isomorphism possible?
I am working on the following homework problem:
Let $\phi$ be an isomorphism from $\mathbb{R}^*$ to $\mathbb{R}^*$ (nonzero reals under multiplication). Show that if $r>0$, then $\phi(r) > 0$.
...
- 1,852
0
votes
2
answers
959
views
$R/\Bbb Z$ isomorphic to $R/(2\pi \Bbb Z)$
I was told that $\mathbb{R}$$/$$\mathbb{Z}$ is isomorphic to $\mathbb{R}/2\pi \mathbb{Z}$ when these groups are taken under addition. Is this always true? I do not specifically see why this has to be ...
- 263