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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
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