Let p : ([0, 1], T1) → ({0, 1}, T2) be the quotient map, arising from the characteristic function on [\(\frac{1}{2}\), 1], where T1 is the subspace topology induced by the Euclidean topology on ℝ. Which of the following statements is TRUE?
1
p is an open map but not a closed map
2
p is a closed map but not an open map
3
p is a closed map as well as an open map
4
p is neither an open map nor a closed map