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Curated by: Dr. Trefor Bazett (643 videos)
Keep learning at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription! What exactly does it mean for a space to be connected? In this video we will contrast the notions of connected, path connected and simply connected for a range of topological spaces such as the topologists sine curve, the torus, and the fascinating Alexander's Horned Sphere. 0:00 Topologist's Sine Curve 1:25 Definition of Connected 3:10 Definition of Path Connected 4:06 Topologist's Sine Curve again 7:24 Simple Connected 9:37 Alexander's Horned Sphere 11:55 Brilliant.org/TreforBazett The animation of Alexander's Horned Sphere was created by Gian Todesco: https://en.wikipedia.org/wiki/Alexander_horned_sphere#/media/File:Construcci%C3%B3n_de_esfera_de_Alexander_con_cuernos.gif Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://beautifulequations.net/pages/trefor COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw ►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS I LOVE (affilliate link): ► https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography