The Klein bottle and the projective plane are the basic non-orientable surfaces. The Klein bottle, obtained by gluing together two Mobius bands, is similar in some ways to the torus, and is something of a curiosity. The projective plane, obtained by gluing a disk to a Mobius band, is one of the most fundamental of all mathematical objects. Of all the surfaces, it most closely resembles the sphere.
This is the seventh lecture in this beginner's course on Algebraic Topology, given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW.
thank you for such clear and simple explanations
madier1000 1 month ago
This is excellent..I wish i had learnt alg. topology that way instead of starting with homotopies, simplicial homology and the same,...
allotrios2 8 months ago
Wonderful work, Professor. The only place where one can learn algebraic topology without going through point set topology. Though, I would like if you could ship out another series of lectures which is more formal than this one, this work is also truly amazing.
akash007ssp 1 year ago