Cross-cap
In mathematics, a cross-cap is a two-dimensional surface that is topologically equivalent to a Möbius strip. The term 'cross-cap', however, often implies that the surface has been deformed so that its boundary is an ordinary circle. This cannot be done in three dimensions, without the surface intersecting itself.
A cross-cap that has been closed up by gluing a disc to its boundary is called a real projective plane.
Two cross-caps glued together at their boundaries form a Klein bottle.
An important theorem of topology, the classification theorem for surfaces, states that all two-dimensional nonorientable manifolds
are spheres with some number of 'handles' and at most two cross-caps.
Referenced By
List of geometric topology topics | List of mathematical topics | List of mathematical topics (A-C) | List of mathematics topics
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