Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I met projective space via a recent class on perspective drawing, believe it or not, but I didn't know that this was the "space" we were using. I came across a more detailed description trawling the net.

In a book on point-set topology that I bought, it describes Euclidean n-space as a field made of (sorry I don't know how to write mathematical symbols yet):

[ {n-tuples of reals}, Op("+"), Op(".") ]

So what is the equivalent set-theoretic description for projective space? I haven't been able to find one anywhere. All I've found is that basically it is constructed by taking a regular plane and adding the 'horizon' line but I want to understand mathematically what it is. Wiki page is confusing as hell. :(

share|improve this question
    
Yes, there is, but this isn't the appropriate place to ask about it; ask at math.stackexchange.com, for example. –  Qiaochu Yuan Feb 27 '11 at 16:30
2  
Sorry - will try stackexchange.com. thanks. –  mathmoggy Feb 27 '11 at 16:35
add comment

closed as too localized by Angelo, Simon Thomas, Qiaochu Yuan, J.C. Ottem, Todd Trimble Feb 27 '11 at 16:51

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

1 Answer

up vote 1 down vote accepted

One definition is that the $n$-dimensional (real) projective space is the space of lines through the origin in $R^{n+1}$. Technically it is a topological quotient of $R^{n+1}$ minus the origin, by the equivalence relation $x\sim \lambda x$ for all (nonzero) vectors $x$ in $R^{n+1}$ and all (nonzero) scalars $\lambda$.

share|improve this answer
    
Hi Aaron - I don't understand why you nave (n+1) as opposed to just n, so clearly my understanding really is more elementary. I'll accept your answer to pass on the points karma nevertheless and re-ask my question on stackexchange as directed. Thanks! :-) –  mathmoggy Feb 27 '11 at 16:38
add comment

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