Is this bizarre space connected??? || Connected vs Path Connected vs Simply Connected

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:Constr ...