Connectedness and path-connectedness
General · Mathematics
Study notes
Q: Is ℚ connected? Is S¹ path-connected? ℚ: ℚ = (ℚ∩(-∞,√2))∪(ℚ∩(√2,∞)): separation: DISCONNECTED! S¹: any two points: arc between: PATH-CONNECTED! Path-connected ⟹ connected ✓. Topologist's sine: connected but NOT path-connected! (Weird counterexample!)