Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I need help on the following problems:

QN1 Consider the map $f:(\Bbb R\times\Bbb R,\tau)\to(\Bbb R,\gamma)$ given by $f(x\times y)=|x-y|$,where $\tau$ is the product topology and $\gamma$ is the usual topology. Find $f(1),f(0),f^{-1}(0)$ and $f^{-1}[0,1)$.

for this problem ,I don’t know how to use the given definition to find say $f(1)$, also I get difficult how to come with $f^{-1}$.

Another one is someone to help me, I read somewhere that the set of rational number $\Bbb Q$ as a subspace of $\Bbb R$ (with usual topology) does not have discrete topology since the point $0$ is not an open set in $\Bbb Q$. Why this argument true?, For me I know that $0$ is rational. Thanks

share|improve this question
1  
f(1) doesn't seem to make sense to me. (Is R the set of real numbers?) The topology on Q is given by 'open balls' (= open intervals) on Q. Can you find a radius r and a midpoint q such that the open ball of radius r about the point q (i.e. the interval (q-r, q+r)) contains 0 and no other points? –  Billy May 11 '13 at 20:05
    
@Billy:yes R is the set of real number,Thanks –  user77362 May 11 '13 at 20:19

1 Answer 1

The number $1$ is not (at least not without further conventions) an element of $\mathbb R\times \mathbb R$, hence I understand why you have problems finding out what $f(1)$ should be.

For $f^{-1}$, you need to find all $(x,y)$ such that $|x-y|$ ...

For the totally unrelated about $\mathbb Q$, note that $\frac1n\to 0$.

share|improve this answer
    
:Yes It confuse me how to do,I need help how to work out that? Is there a way to write 1 in the form XxY?.Thanks –  user77362 May 11 '13 at 20:42
    
No - that's Hagen's point (and mine). The question, as it stands, doesn't make sense. If there's extra information you're not telling us, please do; otherwise, the question is unclear. –  Billy May 11 '13 at 20:54
    
Owkay,Let me find out.Thanks –  user77362 May 11 '13 at 21:04

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.