#mathober day 6: Connected Topology
Learned about the "Topologist's Sine Curve", sin(1/x), defined on (0,1], together with the origin. The question: Is it "connected"?
Turns out that it's neither path-connected (the duck can't reach the horizon) nor locally connected (no matter how small you make the "sun disk", the river that overlaps it will never be one piece) , but still "connected" (there's no gap between river + sun you could cut along). Weird!