# Definition:Projective Space/Real Projective Space

Let $\Bbb S^n \subseteq \R^{n+1}$ be an $n$-sphere.
Let $\sim$ be the equivalence relation defined on $\Bbb S^n$ by:
$x, y \in \Bbb S^n: x \sim y \iff x = -y$
The real projective space of dimension $n$ is the quotient space $\Bbb S^n / \sim$ and is denoted $\Bbb{RP}^n$.