AlgTop2: Homeomorphism and the group structure on a circle

This is the first video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic.

Then we introduce the group structure on a circle, or in fact a general conic, in a novel way, following Lemmermeyer and as explained by S. Shirali.

This gives a gentle intro to the definition of a group. It also uses Pascal's theorem in an interesting way, so we give some background on projective geometry.

This lecture is part of a beginner's course in Algebraic Topology given by N J Wildberger at UNSW.

His YouTube site Insights into Mathematics at https://www.youtube.com/user/njwildberger?ob=0 under user: njwildberger also contains series on MathFoundations, History of Mathematics, LinearAlgebra, Rational Trigonometry, Universal Hyperbolic Geometry, and even one called Elementary Mathematics (K-6) Explained.