# Random question: Is there a set-theoretic description of projective space? [closed]

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. :(

-

## 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.

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
Sorry - will try stackexchange.com. thanks. – mathmoggy Feb 27 '11 at 16:35

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 $\lambda$.