aka projective space, specially when referring to the more general versions in higher dims, or with complex numbers.

Real projective plane

video from diffgeo lectures

its topology. Sphere can provide a Covering

real projective plane is Mobious strip + disk – animation

A model is the Crosscap, i think

video 2

2d projective plane can't be embedded into R^3 (Embedding). But it can be embedded into $\mathbb{R}^4$ (vid)

vid3

Complex projective plane

See Hatcher pg 6