Let X = ℝ in the standard topology. Take the partition X* = {…,(−1,0],(0,1],(1,2],…}. Describe the open sets in the resulting quotient topology on X*.

Let

X = ℝ
in the standard topology. Take the partition

X* = {…,(−1,0],(0,1],(1,2],…}
.

Describe the open sets in the resulting quotient topology on

X*.