What is...cellular approximation for spaces?

Goal. Explaining basic concepts of algebraic topology in an intuitive way. This time. What is...cellular approximation for spaces? Or: My polynomials have cells. Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Disclaimer. These videos are concerned with algebraic topology, and not general topology. (These two are not to be confused.) I assume that you know bits and pieces about general topology, but not too much, I hope. Slides. http://www.dtubbenhauer.com/youtube.html Website with exercises. http://www.dtubbenhauer.com/lecture-algtop-2021.html Cellular approximation. https://en.wikipedia.org/wiki/Cellular_approximation_theorem https://ncatlab.org/nlab/show/cellular+approximation+theorem https://mathworld.wolfram.com/CellularApproximationTheorem.html Stone-Weierstrass approximation. https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem https://en.wikipedia.org/wiki/Bernstein_polynomial Hawaiian earrings and friends. https://en.wikipedia.org/wiki/Hawaiian_earring https://en.wikipedia.org/wiki/Topologist%27s_sine_curve https://en.wikipedia.org/wiki/Shape_theory_(mathematics)#Warsaw_Circle Whitehead’s theorem. https://en.wikipedia.org/wiki/Whitehead_theorem Homotopy groups of the Hawaiian earrings. https://wildtopology.com/2013/11/23/the-hawaiian-earring/ https://mathoverflow.net/questions/163847/are-the-higher-homotopy-groups-of-the-hawaiian-earring-trivial Pictures used. https://wildtopology.files.wordpress.com/2019/12/he.png https://i.stack.imgur.com/yYLkv.png https://math.stackexchange.com/questions/696533/quasi-circle-is-not-contractible Hatcher’s book (I sometimes steal some pictures from there). https://pi.math.cornell.edu/~hatcher/AT/AT.pdf Always useful. https://en.wikipedia.org/wiki/Counterexamples_in_Topology Mathematica. https://demonstrations.wolfram.com/BernsteinPolynomials/ #algebraictopology #topology #mathematics