Cross-cap

A cross-cap or cross cap designates a certain area in mathematics.

On its own, is the cross-cap equivalent to a projective plane. In general, however, described by the term a correspondingly shaped portion of a greater variety, the edge of a Möbius strip is connected to an opening in the manifold so that no edge is. In this form, the cross-cap no longer be embedded without self in the three-dimensional space. Most views of a cross-cap show this on the surface of a sphere.

The property that the cross-cap is not orientable, then transferred to the associated manifold.