Let X= Y∪{(0,y):-1≤y≤1} Y={(x,sin(1/x)): x∈(0,1]}
Let γ: [0,1] →X be a path starting at (0,0). That is, γ is a continuous function, and γ(0)=(0,0). Let A= {(0,y): -1≤y≤1} be the portion of the y-axis that's inside X. Show that γ^-1(A) is a closed subset of [0,1]
