Quick Denotation Question

$\displaystyle R^\times$ and $\displaystyle C^\times$ mean when referred to the following example:

Does there exist an isomorphism from $\displaystyle C^\times$ to $\displaystyle R^\times$.

I have a fairly good idea on how to solving this, but I can't really solve it w/o the ability to read the denotation.

Thanks!

Re: Quick Denotation Question

Quote:

Originally Posted by

**Sw0rDz** $\displaystyle R^\times$ and $\displaystyle C^\times$ mean when referred to the following example:

Does there exist an isomorphism from $\displaystyle C^\times$ to $\displaystyle R^\times$.

I have a fairly good idea on how to solving this, but I can't really solve it w/o the ability to read the denotation.

Thanks!

dual space maybe

Re: Quick Denotation Question

Maybe its an isomorphism between the multiplicative groups of $\displaystyle \mathbb{C}$ and $\displaystyle \mathbb{R}$.

Re: Quick Denotation Question

Quote:

Originally Posted by

**Sw0rDz** $\displaystyle R^\times$ and $\displaystyle C^\times$ mean when referred to the following example:

Does there exist an isomorphism from $\displaystyle C^\times$ to $\displaystyle R^\times$.

I have a fairly good idea on how to solving this, but I can't really solve it w/o the ability to read the denotation.

Thanks!

I would tend to agree with **emakarov** that $\displaystyle \mathbb{R}^\times$ denotes the group of units of $\displaystyle \mathbb{R}$ and similarly for $\displaystyle \mathbb{C}^\times$. So, what is your proof? There is an easy way and a hard way.