notesonly.in

Q: In ℝ² with Euclidean metric, is {(x,y): x²+y²<1} open? Describe B((0,0),1). B((0,0),1) = {(x,y): x²+y²<1} (open disk!)! Open: every point has ball inside ✓: OPEN! Boundary circle x²+y² = 1: not included! ( Balls generate metric topology!)