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Currently Playing: Topology vs "a" Topology | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What exactly is a topological space? Learn through active problem-solving at Brilliant: https://brilliant.org/InfiniteSeries/ Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode This Video was Not Encrypted with RSA | Infinite Series https://www.youtube.com/watch?v=4Tb1q8dSIlI We’ve talked about topology here on Infinite Series. It’s the branch of math where we study properties of shapes that are preserved no matter how you bend, twist, stretch or deform them. And you’ve probably come across some cool examples of these shapes - or topological spaces - like spheres and tori, Mobius bands and Klein bottles. In this episode we discuss the the 3 axioms that underlie all of topology. If you want to dive deeper after watching this episode check out the links below: References: Topology Via Logic by S. Vickers https://books.google.com/books/about/Topology_Via_Logic.html?id=peXBNAEACAAJ Topology by Munkres https://www.amazon.com/Topology-2nd-James-Munkres/dp/0131816292 For the solution to the challenge question check out: http://www.math3ma.com/mathema/2017/12/21/topology-vs-a-topology Written and Hosted by Tai-Dinae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Meah Denee Barrington and Emma Dessau Made by Kornhaber Brown (www.kornhaberbrown.com) Thanks to Matthew O'Connor, Yana Chernobilsky and John Hofmann who are supporting us on Patreon at the Identity level! And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!