Suppose we have a ring-like shape with two broad faces... We cut the ring and make a twist of 180 degrees to produce the world famous Moebius strip. A one-faced shape.
Let's say we cut the shape again and make an infinite series of 180 degrees twists... This would produce a consecutive series of one and two faced shapes... Do these shapes, particularly the one faced shapes, receive any special study in topology? Where can I find info on these?
Thanks!