arguing with a math PhD friend be like (unscripted, unedited)
I asked a math Ph.D. @drpeyam to explain the topologist sine circle (topologist sine curve) from the book "Real Analysis" by Charles Pugh. It is the set of all (x,y) so that x=0 and the absolute value of y are less than or equal to 1 or y=sin(1/x) for x belongs to (0,1]. This is a very interesting curve because it is path-connected but not locally path-connected. What exactly does that mean? Well subscribe to @drpeyam for higher-level math and check out his video here: • Topologist Sine Curve
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