The set of all such lines is itself a space, called the real projective plane in mathematics.

This is also one of the standard models of the real projective plane.

The result is orientable, while the real projective plane is not.

Another such surface is the real projective plane.

Any connected sum involving a real projective plane is nonorientable.

The restricted planes given in this manner more closely resemble the real projective plane.

W-curves in the real projective plane can be constructed with straightedge alone.

Other related non-orientable objects include the Möbius strip and the real projective plane.

The closed surface so produced is the real projective plane, yet another non-orientable surface.

The real projective plane has a fundamental group that is a cyclic group with two elements.

The first case includes all surfaces with positive Euler characteristic: the sphere and the real projective plane.

Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point.

A 3-manifold is P2-irreducible if it is irreducible and contains no 2-sided (real projective plane).

(Similar remarks hold about the real projective plane, but the intersection relationships are different there.)

The sphere, before being transformed, is not homeomorphism to the real projective plane, 'RP2'.

Projectivization of the Euclidean plane produced the real projective plane.

For concreteness, we will give the construction of the real projective plane P(R) in some detail.

The real projective plane, like the Klein bottle, cannot be embedded in three-dimensions without self-intersections.

However, only three of these points may be real, so that the others cannot be seen in the real projective plane by drawing the curve.

Mathematicians commonly refer to the elliptic plane as the real projective plane.

Because the real projective plane covers the sphere twice, it may be represented as a hemisphere around whose rim opposite points are similarly identified.

The case where the coefficients are all real gives the equation of a general circle (of the real projective plane).

But Möbius strips, real projective planes, and Klein bottles are non-orientable.

The combination of affine plane and line at infinity makes the real projective plane, .

Therefore the Boy's surface is homeomorphic to the real projective plane, RP.