Every Hausdorff space has a Riemannian connection which is the potential of a conserved source. An 8-dimensional space in which four dimensions resemble a Klein bottle shows promise for uniting quantum mechanics and general relativity. ...

The Klein Bottle The Klein bottle is another unorientable surface. It can be constructed by gluing together the two ends of a cylindrical tube with a twist. Unfortunately this can't be realized physically in 3-dimensional space. The best we can do is to pass one of the ends into the interior of the tube at the other end (while simultaneously inflating the tube at this second end) before gluing ...

Up: Math Home The Klein Bottle The Klein bottle is the non-orientable surface with Euler characteristic equal to 0. A Klein bottle can be made from a rectangular piece of the plane by identifying the top and bottom edges using the same orientation, but identifying the left and right edges with opposite orientation (as in the formation of a M bius band). The first step forms a tube, but the ...