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. :(



Random question: Is there a set-theoretic description of projective space?
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 $\lambda$.


